Kane looks set to finish the tournament as the top scorer with six goals, but he has gone off the boil somewhat since plundering five goals in his first two games.
The Spurs star has failed to record a shot on target in his last three appearances for his country, though Southgate move to back his forward after it was suggested that he was exhausted in Saturday's defeat.
"Today is the seventh game in a short period of time, and we've had incredible physical demands and emotional demands on the least experienced team in the tournament," Southgate explained.
"It would be wrong to judge any player on today's game, if their energy levels were short. I think he has captained the team exceptionally well, he has led the culture we are trying to create.
"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.
"I'm immensely proud of the players. All of them. And they should be proud of themselves because they've achieved an equal high in terms of tournament performance that any English team that's had to come abroad for a tournament has achieved."
Whilst southgate was unwilling to criticise individuals, he did single two players out for praise in the form of goalkeeper Jordan Pickford and defender John Stones.
"I thought Stones was absolutely outstanding and Pickford has had a wonderful tournament," he added.
"Today was always going to be a really difficult game.
"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."