'We left everything out there'
England were hoping to reach a first World Cup final since 1966, but let an early lead slip to lose 2-1.
"I think in the first half we were really good and maybe we could have got another goal," Southgate told 'ITV'.
"I can't ask for more from the players. I think knockout football is about fine margins and when you have good spells against fine sides you need to take your chances.
"Tonight we weren't quite there but we will learn from that. We left everything out there."
Croatia will be the smallest nation to play the final match of a World Cup since Uruguay won the 1950 tournament when they face France on Sunday, after recovering through a second-half Ivan Perisic volley and Mario Mandzukic's winner deep into extra time.
"It's great for us and for smaller countries it shows that if you dream and have the character and work hard, dreams are possible," said former Croatia coach Slaven Bilic in his role as an ITV pundit.