The stance, which is in support of the Black Lives Matter movement but is separate to the political organisation of the same name, has prompted much debate around the sporting world.
But Southgate spoke passionately in a press conference on Saturday in support of his players’ decision to continue presenting a united front against all forms of discrimination.
“In essence people are booing their own team,” he said.
“The most important thing for our players is to know that we are totally united on it,” he said.
“We are totally committed to supporting each other, supporting the team. We feel more than ever determined to take the knee through this tournament.
“We accept that there might be an adverse reaction and we are just going to ignore that and move forward.
“I think the players are sick of talking about the consequences of: ‘Should they? Shouldn’t they?’ They’ve had enough, really.”
Midfielder Jack Grealish said the booing was something “we don’t want in football” after Wednesday’s 1-0 win over Austria, while Kalvin Phillips said he was “confused and disappointed” by the fans’ behaviour.
England face Romania in their final warm-up game in Middlesbrough on Sunday before playing Croatia, Scotland and the Czech Republic in Euro 2020 Group D matches at Wembley.
Southgate said he would not discuss the issue again if fans booed once more, because “we don’t want to give oxygen to those people.”
The Three Lions’ stance has been criticised, with Conservative MP Lee Anderson vowing to boycott their matches over their decision to take the knee before kick-off.
Meanwhile, fellow Tory MP Brendan Clarke-Smith said Southgate’s comments were “an insult to fans’ intelligence”.