The Three Lions had to settle for finishing fourth after goals from Thomas Meunier and Eden Hazard saw Belgium inflict a 2-0 defeat in their third place play-off St Petersburg.
Southgate feels his players showed plenty of positive signs in Russia and expects his team to improve significantly.
"We are competitive in every game. We've overcome a lot of landmarks that we needed to," Southgate told ITV Sport.
"To finish in the top four is probably above where we are currently. Huge credit to the players because they deserve every bit of praise that they get when they go back.
"You look at the number of caps the Belgium players have and at the age of the squad; they're at their peak, this was really their big tournament.
"We're nowhere near our peak yet, we've know that right the way through."
Belgium the better side
England were second best for most of Saturday's game and Southgate admitted the better team won and believes Belgium may still have regrets over their semi-final loss to France.
"I think they're a better side than us. The reality is we've had a day less to prepare and recover and I think it was just a game too far for us," he added.
"They are a top team and great credit to them, they'll probably be thinking they should have gone further than they did.
"From my point of view, our players have given absolutely everything right the way to the final whistle."
England captain Harry Kane failed to score for the third successive game but remains on course to win the golden boot having hit six goals earlier in the tournament.
The Tottenham striker challenged his team-mates to repeat their form in future competitions.
"The lads couldn't have given any more, it's been a tough tournament, Belgium are obviously a good team," said the 24-year-old.
"We've closed it (the gap to the top teams) but today shows there's still room for improvement. We're not the finished article yet, we're still learning, we're still getting better. This is the level we've got to try and stay at now."
Martinez happy with third
Belgium's victory means they recorded their best finish at a World Cup, bettering fourth place at Mexico '86, and coach Roberto Martinez said his talented group of individuals had proved they could play as an effective team.
"It's all about that achievement (finishing third), these players deserve that," said the Spaniard.
"There's a lot of talk about a group of players with talent takes you somewhere, I think what we've seen in this World Cup is these players didn't want to rely on the talent any more, they wanted to rely on working as a team.
"They wanted to make the country proud and wanted to make every single Belgian Red Devil fan extremely proud, and that goes for them."
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