Price was one of four Scotland players who made the gesture at Twickenham during a pre-match moment of reflection aimed at supporting the fight against racism and discrimination in rugby.
Taking a knee has become commonplace at major sporting occasions since last summer in a bid to highlight global race issues.
Price, team-mates Jonny Gray, Chris Harris and Cameron Redpath and 11 members of the England squad all kneeled before Scotland’s 11-6 win.
The fact that the majority of the Scotland players did not take a knee has provoked a backlash.
Coach Gregor Townsend and the Scottish Rugby Union have stressed their commitment to tackling racism and discrimination in rugby but have also said their players had the right to choose how they showed this support.
The pre-match situation at Twickenham was confused by mixing the anti-racism message with a tribute to those who had died during the Coronavirus pandemic, including captain Sir Tom Moore, and former England international players who had passed away in recent weeks, including their ex-captain, John Pullin.
“We were told beforehand that there would be a round of applause for Sir Tom and everyone who has sadly passed away due to Covid, followed by a moment of reflection around racism in sport and in general, and that it is very much individual,” explained Price.
“For me personally, I’ve never taken a knee in any of the games I’ve been involved in before, it was never a part of any of the build-up to Pro14 games or in the Autumn Tests.
“On the day, I felt it was right to take a knee, but at the same time I could have stood like many of the other players and team-mates did and just had that moment of reflection. I feel like there are different ways to do that.
“I don’t think there is too much to read into that. Everyone was reflective, everyone was respectful, and then we got on with the anthems and the game.”
Jamie Ritchie, the Scotland flanker, was one of the players who remained standing and admitted he has been taken aback by the reaction.
“It’s all been a little bit of a surprise to be honest,” said the Edinburgh forward. “We weren’t told before the game ‘we’d like you to kneel’ or ‘we wouldn’t like you to kneel’, so it was down to personal choice.
“I don’t think anyone who didn’t kneel was disagreeing with anything that was being put forward and I think it is 100 per cent right that rugby is acknowledging the anti-racism movement, and I completely agree with that.
“I think guys standing in quiet reflection of that is in full support of it. Whether boys did kneel or didn’t kneel, it wasn’t something we discussed before the game, it was completely down to personal preference. Anyone who kneeled I’d back 100 per cent and anyone who stood I’d do the same.”