The touching moment comes as Southgate and his players are being called national heroes by supporters who thanked them for restoring the nation's pride in its football team during the 'best three weeks of our lives'.
Tearful stars including Jordan Pickford, Marcus Rashford, Kieran Trippier, Harry Maguire and Kyle Walker were comforted by their partners, parents and children after their extraordinary and unexpected World Cup adventure in Russia came to an end.
On the pitch their visibly emotional manager hugged every player, most of them in tears, as the 10,000-plus English fans in the stadium cheered them and sang 'Three Lions' and Oasis' 'Don't Look Back in Anger'.
This morning, many of the stars took to social media to explain that they were 'heartbroken' and left feeling 'gutted' after the side's exit, while others praised Southgate for restoring pride in the national team.
Defender Kyle Walker called for England to 'keep the unity alive, I love you', as his teammate Marcus Rashford tweeted a photograph of himself with his manager with the caption 'you’ve brought belief and the love of football back. Thank you boss from the whole nation'.
Last night's defeat - watched by 26.5million people on ITV, making it the most watched event in Britain since the London Olympics in 2012 - left many supporters sobbing as England lost in extra time.
Southgate embraces his wife Alison in the empty seats behind the dugout in Moscow Luzhniki stadium after the loss
England fans cling to each other in Hyde Park last night as they come to terms with yet another World Cup defeat
England stars Kyle Walker and Jesse Lingard were among those to speak of their honour and gratitude at representing their country during this World Cup
National captain Harry Kane and Kyle Walker expressed their pain at getting knocked out of the tournament last night as they thanked Three Lions fans for their support
England striker Jamie Vardy was among the stars to express his gratitude for the England fans, adding 'thank you to each of you who have been there each step of the way'
England manager Gareth Southgate embraced his wife of more than 20 years after the defeat to Croatia last night
This England fan's tear-stained face sums up the pain of yet another World Cup defeat for the team last night
Two fans embrace in Hyde Park in London as they consoled one another after the 2-1 defeat to Croatia in Moscow (left) - around two hours earlier they were ecstatic as England scored (right)
England manager Gareth Southgate comforted all the players before he embraced his wife Alison after the defeat to Croatia last night
Dele Alli kisses his girlfriend Ruby Mae in the crowd after a see-saw semi-final where England were on top but lost
Some even suggested that England's heroes should be given a parade to honour their unexpected run in the tournament, a notion quickly shot down by the FA which said it had no plans to hold an official presentation.
Hopes were high after Trippier's stunning free kick sent the nation crazy in a first half where the team missed at least two more excellent opportunities to kill off the game.
But Croatia, led by star player Luca Modric, fought their way back and made England pay for their scorned chances, scoring once with 20 minutes to go and again in extra time to break English hearts.
Back home thousands of bereft fans struggled to come to terms with yet another defeat in the final stages of a major tournament.
Today many fans woke up with a mix of deep sadness and pride, with England now focused on regrouping ahead of the third place playoff with Belgium on Saturday.
Theresa May, who was unable to watch the game due to the Nato summit, heaped praise on Southgate and insisted everyone should be proud of what England achieved.
A spokeswoman for the Prime Minister said: 'She thinks that he led the team fantastically and that the whole country should be proud of how far England got.'
Meanwhile, Chris Pit tweeted: 'Woke up still gutted but thank you Mr Southgate for bringing belief, pride & passion back to the England team', Sam Phillips wrote: 'Absolutely gutted! What a journey! You gave us all hope...one day it will come home'.
Alan Kemp said: 'Woke up today with a bit of a sore head and sore heart but a quick cuddle with my England flag just reminded me what we achieved and how proud I am of this team'.
Rob Jones wrote: 'So it’s not coming home then...except, it still is. Football doesn’t mean a trophy or being the best. It’s about the spirit of the game, playing the game right, making your fans proud. England did that. So, it’s coming home'.
Tom Neary said: 'Still gutted, although the trophy isn’t coming home it feels like football is. True pride in the national team, can’t wait to see them in the Euros in 2 years time'.
The 47-year-old also saved a cuddle for his son Flynn, left, and daughter Mia, right,
Jordan Pickford breaks down with his girlfriend Megan Davison after the 2018 FIFA World Cup Russia Semi Final match between England and Croatia
Kyle Walker kisses his daughter as England after the World Cup exit in the Luzhniki Stadium, Moscow, last night
Kieran Trippier of England speaks with his clearly upset family following England's defeat to Croatia in Moscow as the squad bids farewell to making the final
The 2-1 loss was too much for this fan in the Luzhniki Stadium as he burst into tears after the final whistle. Back home one young England fan was comforted by his mum at the Castlefield Bowl, Manchester after the loss to Croatia
England fans have reacted with grief and pride after the team failed to make the big step to the final on Sunday
The England squad's wives and girlfriends draped their arms round the players following the 2-1 defeat at the Moscow stadium.
Players fell to their knees in tears at the final whistle while millions of people watching at home were also left weeping after coming so close to getting to the final.
Megan Davison was seen sitting next to tearful goalkeeper Jordan Pickford, as his loved ones consoled him while Harry Maguire was comforted by Fern Hawkins and goal-scorer Keiran Trippier sat with his family in the stands.
Kyle Walker was comforted by his young daughter while Dele Alli embraced and kissed his girlfriend Ruby Mae.
The team didn’t get back to St Petersburg until 8am today. Footage was seen of the coach arriving at the team hotel with some players asleep with hoodies up. They are expected to sleep in this morning and have massages and pool exercises later on. Trippier likely to fly home tonight for treatment.
Back home, a staggering 30,000 people descended on Hyde Park in London where the Lightning Seeds treated the crowd to a rendition of Three Lions.
Stars including One Direction's Louis Tomlinson and London Mayor Sadiq Khan was also among the crowd.
Extraordinary footage showed the crowd go berserk after England scored with pints of flying everywhere, but by the final whistle it had all ended in tears.
Millions more watched the game in pubs and other fan festivals up and down the country.
At Millennium Square in Leeds thousands of fans, many wearing replica T-shirts, enjoyed the match.
Many linked arms to sing the national anthem, with the venue filling up completely 45 minutes before kick-off.
England were beaten 2-1 after extra time by Croatia in their first World Cup semi since 1990 - and Harry Kane admitted it hurt but thanks the millions who supported them
Marcus Rashford kept his tweet short, simple and effective after England's heartbreak
Harry Maguire, Jesse Lingard and Harry Kane also expressed their thanks to the fans
Reserve goalkeeper Jack Butland posted a picture of the England players with the crowd
In Bristol thousands of football supporters gathered at the city’s fan zone to watch the match. And more than 8,000 fans were at Castlefield Bowl in Manchester.
After the defeat, Prince William offered his support to the England team. He tweeted: ‘I know how disappointed you must feel right now but I couldn’t be more proud of this team and you should hold your heads high.
‘You’ve had an incredible World Cup, made history, and gave us fans something to believe in. We know there is more to come from this team. W.’
Theresa May said: ‘Wasn’t to be this time but it’s been a great journey that’s made the country proud. We’ll be flying the flag on Saturday. Three Lions.’
Sir Geoff Hurst, a World Cup winner with England in 1966, said at the launch of Deliveroo's edible pitch, said: 'Even though Harry isn’t lifting the trophy on Sunday, we should be proud of our boys. The young team have emerged as heroes, especially Pickford, he has surpassed my expectations.'
Speaking to ITV after the match, captain Harry Kane said: ‘It is tough. We are gutted. We worked so hard. The fans were amazing. It was a tough game.
‘It hurts a lot and we are going to hurt for a while, but we can hold our heads up high. It has been a fantastic journey and we got further than anyone thought we could have. We thought we were good enough to go on and win it. The next step now is to go one further. We have to dust ourselves down and be proud of what we achieved. Then we go again.’
Fans who made the journey to Russia spoke of their disappointment but praised the team for exceeding expectations. Salesman Peter Wood, 63, from Bristol, said: ‘I’m proud of this team and believe they’ll be back even stronger next time.
‘We were given no chance at the start of the tournament yet somehow got to within touching distance of the final. That’s a huge achievement.’
England fans could not believe their eyes as a goal from Croatia took the game into extra time in the second of the semi finals
England fans struggled to hide their anguish as the game went to a draw and the extra time whistle blew. Fans were left gutted in Nottingham Castle (left) and Flat Iron Square (right)
England fans burst into tears after the game tonight, with one face-painted man quick to comfort his companion watching at Ashton Gate Stadium in Bristol
Fans' anguish: Men sat in silence along the roadside in Nottingham just hours after jubilant scenes in the English city
Disappointment for England as Gareth Southgate's team failed to secure the win the fans had desperately hoped for at home. Pictured: Flat Iron Square in London
One fan in Birmingham was pulled out of a canal following the match after apparently jumping in as a reaction to the defeat
Another woman in Liverpool was slumped up against a wall after the defeat as a friend stood over her
Bed shop owner Colin Whiting, 48, also from Bristol, said: ‘It’s been a privilege to see this team come so far and make us all so proud. But they’ve fallen after bringing us so close to a World Cup final after more than 50 years.’
Insurance broker Tom Reynolds, 30, from London, was stoic: ‘No one gave us a chance in hell at the start of this – and it was all about managing expectations.
‘But it’s been an absolute privilege to support these lads.’
Coffee shop boss Conor Ravenscroft, 25, from Bristol, said: ‘They’ll be back stronger next time.’
Former England striker Gary Lineker said: ‘Utterly choked, but this young side gave absolutely everything. It’s a huge step forward and they’ll only get better.
‘They can hold their heads high, they did our country proud. Congratulations to Croatia.’