Gomez started on the bench for the Euro 2020 qualifier against Montenegro, while Sterling was dropped from the matchday squad entirely after his bust-up with the centre-back.
Southgate had affirmed Gomez's innocence in the incident when explaining Sterling's absence earlier in the week, yet there were audible boos as the Liverpool player replaced Mason Mount in the second half at Wembley.
The episode put a dampener on a hugely positive outing for England, as they won 7-0 to clinch qualification.
And Southgate was baffled by the supporters' jeers, telling Sky Sports News: "No, I don't understand it. No England player should ever be booed.
"We're a team, and Joe's done nothing wrong, absolutely. I've made that clear earlier in the week. I don't really understand that.
"He and Raheem are very close, and the whole team are very close. We don't want to see anybody treated in that way."
Southgate explained his decision to bring on Gomez was down to a desire to give him more minutes, albeit without putting the 22-year-old through an "upsetting experience" as he entered the pitch.
"I'm sure [I will have to talk to Gomez], because as a young man, that's an upsetting experience," he said.
"For me, the reason for putting him on was because he's been with us for September and October and we haven't got him into the games. Tonight was an opportunity to do that."
Pushed for a message to the England fans involved, Southgate replied: "No, it's done. It's done. We move on. I've said what needs to be said. It's for me now to make sure that Joe's okay."
Captain Harry Kane - who scored a hat-trick - agreed with Southgate, adding: "Yeah, to be honest, I don't think any England player should be booed. It's a bit confusing as to why - I can't get my head around it.
"We stick together as a group. Joe is a top lad, very strong mentally, and for him, it's a very proud moment to wear the England shirt."