The Manchester City defender was decisive in the defeat as one error was taken advantage by the Dutch to swing the game in their favour.
"I think we've had some players who, at the end of the season, have found it difficult in terms of amount of minutes on the pitch - and others having the complete opposite," Southgate said.
"I think fatigue has played a part tonight, a lack of match sharpness. I'm asking them to play in a way that puts them under huge pressure at the back.
"If we didn't play that way, we wouldn't have got to the semi-finals we've got to, and we would never progress to being a top team because you saw the way Holland played that way as well.
"They also made a really poor error at the back. But I have got to be there to support John because he's going to get criticism after tonight.
"But himself and Harry (Maguire), the way we ask them to play, they take huge strain of the game on their shoulders and they're incredibly courageous to do that.
"So, that's the way I believe they can play and we should play, and we didn't lose because of how we wanted to play. The errors were uncharacteristic, really, and not errors that we would make.
"I've got to not overreact to those things and I have got to be there to support them in what is a difficult moment for everybody."