But he believes even brighter days lie ahead for the third-youngest squad on show in Russian Federation.
"I was back in my hometown".
'It's really painful at the moment but I'm proud of the players, the way we played and the strides they've taken, ' said Southgate.
Croatia, who have reached the final for the first time in their history, will play France on Sunday.
In their run to the last four, England re-engaged with a fanbase disaffected by decades of failure at worldwide tournaments, most notably in a humiliating exit to Iceland at Euro 2016.
He said: "They were the better team, that's all that happened".
"We started slowly, but we showed our character just as in the previous two knockout games when we were a goal down".
Southgate has emerged as a leader - he was already a legendary figure as a player, and now he is well on his way to becoming that as a manager. It's the talented France team that has put all of the talent together and improved in the group stage against a Croatia team whose veterans have stepped up big to pull off a surprising run to the final. "Everybody knows how close our team is and that all comes from him".
The Telegraph's front page called for England to "Hold your heads high" while the Guardian captured supporters' mood with the headline "The hurt goes on". This past month, I've seen videos going around, photos been sent to me. That's why we want our punters to wear waistcoats in tribute to the man himself.
Southgate's team of 23 has been revolutionary in the sense, that unlike the gold superstars of the past, this team is tied on a bond of brotherhood and the spectacle which they have presented in Russian Federation will make it easier for the next generation to follow them. "We've proved to ourselves and our country that is possible".