Sterling has been the subject of a tabloid controversy this week after he was pictured with a tattoo of an assault rifle on his right leg .
"In fairness to him, he wanted to apologise to the group, explained his commitment to the team, and it’s done," Southgate told reporters.
"Everybody moved on. That's part of the long discussion we had when we went for a walk.
"He was given off until the Tuesday night and he arrived on the Wednesday morning. So, he was late. That was dealt with. And we discussed it as a group and moved on.
"There was a mix-up on flights and a connection. We haven't hid anything on that. I think we said he was due to meet on Tuesday night but missed that.
"We know the world we live in. Nothing stays private. So if those situations happen, they are going to be out there. There there is a requirement to answer questions on them, and the possibility they become a bigger issue than they might."
Sterling is expected to be one of England's key players in Russia and Southgate was unwilling to offer details on what punishment, if any, the attacker was given.
"I had a discussion with the player, we come to an agreement. And then I have to say, he's trained brilliantly all week," Southgate said.
"He's so keen for this tournament to be a success for him and the team. There was nothing intentional in his lateness.
"But, of course, I'd given him a bit of extra time so he understood why it was more important to get back earlier than he was able to."