England, and six other European countries, were threatened with sanctions by the sport's governing body if they wore the rainbow captain's armband, which was designed to raise awareness of LGBTQ+ discrimination in the country.
It is just one of a number of issues that the World Cup being in Qatar has highlighted, with migrant worker treatment and women's rights also being discussed.
Germany decided to cover their mouths in protest at FIFA's ban, but England boss Southgate said they will not react to each country's individual acts.
He told talkSPORT: "I'm not quite sure where we are with it now because we know totally what we stand for as a team.
"We've spoken for months about the issues here and what we don't want to be falling into is feeling the need to react to every different country doing their thing.
"Australia produced a fantastic video, and great credit to them, but I don't think we need to produce a better video because we want to be seen to be doing something.
"At some point you have to be confident in what you stand for. I'm totally calm with that side of things.
"I'd have liked to wear the armband but that has proved not to be possible. There are a lot of other things we've been doing for migrant workers and pushing behind the scenes for change with FIFA.
"We are not going to please everybody even if we did something, and I'm not quite sure what that would be, I don't think that would please or be enough for everybody anyway.
"There comes a point from myself and the players when we have to remember why we are here and we are talking about the issues still, which is the most significant thing.
"The symbolic things would be good, maybe there's something that could be done further down the line, I don't know what that is, other people have to be thinking about those things because I've got a limited bandwidth and spending a lot of time on those issues, which is taking me away from football issues at times."
And there are plenty of footballing issues that Southgate will be dealing over the coming days and weeks.
England had a brilliant start with a 6-2 victory over Iran and top Group B after one game. Southgate was less than impressed that his side gave away two goals and has revealed what he has since told his players.
He said: "I've actually said well done because I've also got to balance if you'd said to me seven days ago we'd be three points, and plus four goal difference, then I'd be really happy.
"The point immediately after the game is that we know the level that would be needed tomorrow to win the game and we've conceded too many goals.
"Great we've scored so many, but we've also got to get both ends of the pitch right if we're going to be serious contenders here."
Their next game is against the USA on Friday, who drew 1-1 with Wales in their first group match.
Assessing their next opponents, Southgate added: "Pretty much what we've seen. High energy, athletic midfield, speed in their forward positions. I don't think we'll see anything different.
"They will be highly motivated for the game, they have quite a few players who play in the Premier League.
"I think it will be a strong test and we will need to be good in all aspects of our game."
The Three Lions were also given a boost this week with the news that captain Harry Kane would be fit following a scan on his ankle.
He added: "He did some work away from the group yesterday [Wednesday], partly because of reloading anyway. We just wanted to give him an extra day to recover, but he's absolutely fine."