Manchester City attacker Sterling was dropped by Southgate after he confronted Liverpool defender Gomez in the England canteen a day after the Reds had beaten City 3-1 in the Premier League on November 10.
"They definitely came close together," Southgate told Sky Sports Football.
"I think Raheem's message once Joe had received the adverse reaction at Wembley was a really powerful one. I think that really brought some closure on the whole episode.
"We're dealing with young men who are going to be emotional at times, and part of the strength of some of players is that edge that they have, I understand that.
"Some you've got to guide them through these things, and I think through that adversity we're stronger as a group for it."