England return to Middlesbrough's Riverside Stadium on Sunday for their final warm-up friendly against Romania, four days after facing Austria in front of around 7,000 fans with many choosing to boo the players as they made the gesture before kick-off.
Southgate held a meeting to discuss the situation and revealed the squad's position at a news conference on Saturday afternoon.
"I think we have to accept there could be elements of the crowd that boo," Southgate said. "That would be hugely disappointing for us but we are prepared to go through that so whatever happens we are adamant that's the stance we are going to take throughout the tournament. If it happens in future matches, we won't be discussing it after because we don't want to give oxygen to those people.
"The only reason I called the meeting was that I want to be able to represent the players correctly when I speak about it and I was concerned that what happened could affect young players in particular when it happened immediately before the kick-off.
"I'd have been confused and I'd have been... I don't know how I would have reacted as a young player, but in essence people are booing their own team. I don't really understand that. If you don't agree with the situation then you don't have to applaud or you don't have to do anything.
"But to boo your own team is a very strange response in my mind. I wanted to gauge that the players were happy to continue. There is an acceptance that this gesture is waning in its impact because we have been going now for a season but I think ahead of a European Championship where the games are going around the world, that moment just before the kick-off which will be shown everywhere, will have a significant impact.
"If we can affect only a handful of people then we will have made the world better for others. I think we'll affect more than a handful of people and for that reason it is worth us continuing."
"I think those people should put themselves in the shoes of those young players and how that must feel. If that was their children, if they are old enough to have children, how would they feel about their kids being in that sort of situation," Southgate added.
"The most important thing for our players is to know that we are totally united on it. 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."
Hopes are increasing that Manchester United defender Harry Maguire and Liverpool midfielder Jordan Henderson could be available for England's opening Group D match against Croatia on June 13 as they recover from ankle and groin injuries respectively.
"Our medical team are pleased with Harry's progress and particularly over the last couple of days but all of the guidance is that he should be available and it is a case of when he can slot back into training with the group and how quickly we can progress him," Southgate said.
"Of course there is always that risk with any injury that you only have to have one minor setback and two or three days here and there really affects those timelines."
Henderson is likely to be involved against Romania as he targets his first competitive action since February but his Liverpool teammate Trent Alexander-Arnold has left the camp after being ruled out of the tournament with a thigh injury.
"It is heartbreaking for any player to get to the eve of a major tournament, be named in the squad and then miss out through injury. You know how rare these opportunities are and even though he is a young player who is going to have his opportunities again -- I firmly believe that -- that's a really difficult moment for him and a big disappointment for us as well," Southgate said.
"The one thing I was pleased about was that immediately after the game, I didn't like the look of the injury but at least it sounds as though he should be fine for pre-season and next season. That is a very small positive in the situation he is in."