Having clashed towards the end of Liverpool's 3-1 win against fellow Premier League title challengers Manchester City on Sunday, a still simmering Sterling was involved in a fracas with Gomez at St George's Park the following day.
The incident took onlookers aback and the 24-year-old Sterling admitted "emotions got the better of me" in a late night social media post that followed the Football Association confirming the forward would sit out the Montenegro qualifier.
Sterling stayed with the group and apologised to team-mates at a meeting on Monday night, then trained as usual the following morning.
Gomez appeared to be sporting a cut close to his right eye in the session but Southgate remained tight-lipped on that - one of numerous queries he batted away at the hastily-organised press conference.
"Raheem in his post last night explained for a very brief moment his emotions ran over," he said. "It would be correct to say that's not the same for Joe.
"We are dealing with a very young squad in a sport where emotions often run high. These things happen in football. My priority is always the care and wellbeing of all my players. All my players.
"Then you have a decision to make as to whether there needs to be something further, which is my reasoning for not selecting Raheem for the game on Thursday."
Southgate said the whole squad is now interacting as normal and the punishment would be the "end of the matter'", while the England boss took a conciliatory tone when asked if he was disappointed in the forward's conduct.
"I love all of my players," he said. "We are like a family and all family have disagreements.
"Most important for any family is to come through those disagreements and work through them. I don't expect as a manager to never have to deal with things that are unexpected or difficult.
"It's part and parcel of the job and part and parcel of working with elite players. Our focus now is to move forward.
"The reality is I'm not prepared to go into details. There is enough conjecture and opinion and talk out there and we don't need to add to it.
"As a group we've decided the best way forward and we're in agreement on that. We move on from there."
Southgate repeatedly refused to go into details about either the incident or fallout, but it is believed some England players found the response a bit heavy-handed - something that contradicts the initial statement made on Monday.
"It's not for me to discuss the details of the incident, so I think there's nothing to be gained from any further discussion on that," said the England manager, who spoke to his leadership group and staff about a suitable punishment.
"In the end, I always have to find the right solution for the group and for how we will work moving forward.
"That's a very difficult line. You try to be fair at all times, like with all the players. I won't always get that right, but in the end I'm the manager.
"I've made a decision and I think it was appropriate for how we want to work moving forward.
"For me it was important that, of course Raheem is a very important player for us, but I felt it was the right thing."