"I love all of my players. We are like a family. The important thing is for a family to communicate and work through problems," said Southgate.
"I don't expect as a manager to not have to deal with issues."
Sterling admitted "emotions got the better of me" during the incident.
The Manchester City forward, who was involved in an altercation with Liverpool's Gomez in his side's 3-1 Premier League defeat on Sunday, has been dropped for England's Euro 2020 qualifier against Montenegro on Thursday.
Southgate confirmed that Sterling was the aggressor in the incident at the team hotel.
"Raheem in his [social media] post last night explained for a very brief moment his emotions ran over. It would be correct to say that's not the same for Joe," he added.
At a team meeting on Monday night, Southgate, Sterling and Gomez all spoke as the manager decided on the appropriate action to take.
"In the end I have to find the right solution for the group," added Southgate.
"That's a difficult line, you try to be fair when dealing with all players. I won't always get that right but I am the manager.
"Raheem is very important for us but I felt it was the right thing."