Politicians have waded into the debate with one Conservative Member of Parliament, Lee Anderson, claiming he will boycott watching England's games at Euro 2020 claiming "this is not the way" to stamp out racism.
Southgate held two meetings with the players to discuss whether they would continue throughout this summer's tournament and there was unanimous support for carrying on.
England face Croatia in their opening Group D match on Sunday and Manchester United defender Shaw said: "It is really simple. Jordan [Henderson] said it the other day. We've had discussions about it, we all chose what we wanted to do and we all agreed it was the right thing to do to carry it on, taking the knee. It is as simple as that. We will keep doing it, we believe in that and we won't stop."
In the same news conference, Shaw also claimed his United teammate Harry Maguire is improving on a daily basis as he recovers from his ankle injury but stopped short of indicating whether he could be fit to play Croatia this weekend.
"He's a massive part of this squad, whether he is playing or not," Shaw said. "I haven't really spoken to him too much about his injury. I don't want to pepper him with questions. He is going along with his rehab. He is getting better day in, day out. There are positive signs but I couldn't say when he'll be back. Obviously we would like him to be back as soon as possible but that's down to him and the physios so we'll let them to do their work."
Shaw hopes he can "put things right" with England this summer following United's Europa League final defeat to Villarreal last month.
United lost 11-10 in a penalty shoot-out to leave them still without a trophy since 2017. Shaw added: "It was a massive blow. I think we progressed very well in the season but we weren't quite there at the end.
"Of course, there's extra determination and motivation. That was the lowest of lows that could have happened personally for us this season.
"Luckily we've got a few weeks to put things right and maybe go out on a high after the season. That's out of the window now, we need to forget about it. It is a new tournament, a new focus. I need to be 100 percent here and not think about anything else."