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".
England arrived at this World Cup with the least experienced squad in terms of caps, but Southgate said the agony of losing was just as strong despite surpassing limited expectations.
"It was a tough game, a 50-50 game, I'm sure we'll look back at stuff we could have done better but we worked as hard as we could".
Roberto Martinez's side, who were beaten 1-0 by France in the last four, topped Group G ahead of England after an Adnan Januzaj goal settled a low-key encounter in Kaliningrad.
He'll now finish his trip the way it started, by watching England face Belgium - but this time in Saturday's third place play-off.
"And they now see playing for England as enjoyment, fun and not feeling under siege".
"Hopefully.in the next tournaments we can [go] one step further and it will feel a lot better". "There's an energy and connection that's back".
"Meeting and speaking to the players has been a great experience", he said.
Grabar-Kitarovic said she would probably give a Croatia jersey to her French counterpart Emmanuel Macron after sending one to Russian President Vladimir Putin and giving one to British Prime Minister Theresa May earlier in the tournament.
And finally, on the 109th minute, it was Croatia that took home the win. I think the football has brought the nation together, people are going to pubs and celebrating, and that's what football should be about.
Southgate, part of the England team beaten in the semi-finals of Euro 96 when he missed the decisive penalty against Germany, reflected with pride and optimism on Russian Federation 2018.
"I must say the support we've had from home and the feeling of support is vast". "It's very hard to put that into context and a bit too soon really, because I think you have to suffer the result a little bit".