Croatia defeated England Wednesday in a semi-final match and will make its first-ever appearance in the World Cup final against France Sunday.
He particularly underscored the strong efforts of center-back John Stones, goalkeeper Jordan Pickford and striker Harry Kane.
Back home Sir Geoff Hurst, the 1966 World Cup final hat-trick hero, said: "We should be proud of our boys".
Southgate claimed that despite ranking fourth at the tournament, England were "not a top four team yet", though he reiterated he was proud of his team's progress during the tournament.
They could also have a Golden Boot victor in their midst given the fact Harry Kane's six goals put him in a strong position ahead of Sunday's final - not that it makes the captain immune from criticism. "We played one of the best teams in the world with individual talent which is incredible, and we had only two days to get ready for it".
England manager Gareth Southgate also felt there was more to come from his players in future, insisting: "We have gone beyond what we thought was possible".
"Today was always going to be a really hard game".
"There was a lot said about the relationship between our countries, but when we spoke, we saw the sincerity in that relationship on all levels".
"We're probably a little bit short on big-game experience, a bit short on number of national caps and we're a bit young for what a winning national team looks like".
"And although we can talk about having a more comfortable route to the semi-final - and for sure we did - but we've had those routes in the past and not got to the point we have. He (Kane) has captained the team exceptionally well, he has led the culture we are trying to create". "Thank you to the journalists, who have asked the correct questions and we hope that you enjoyed it".