Sterling and Gomez became embroiled in a media storm following a bust-up at the beginning of the international break.
Southgate dropped Manchester City star Sterling for Friday's Euro 2020 qualifying victory over Montenegro, a match partially overshadowed by the boos that greeted Liverpool defender Gomez upon his second-half introduction at Wembley.
The "upsetting experience" for Gomez, as Southgate termed it, prompted Sterling to issue a social media statement accepting "full responsibility" for the spat and defending his team-mate.
An eventful few days took another unexpected turn on Saturday when Gomez pulled out of the squad due to a minor knee problem, but the Three Lions boss now hopes to move forward without further scrutiny of squad harmony.
"You couldn't make it up, really, if you tried," Southgate said of Gomez's injury, which rules him out of Sunday's game against Kosovo.
"He's absolutely fine. He took a clash of knees [on Friday]. We scanned it just to be certain and I think he'll be fine in a couple of days, but he wasn't able to train."
Southgate continued: "We actually ended up having a chuckle this morning at the ridiculousness of him having to go home in the way he did.
"It's been a difficult week for him but one that will make him stronger and one that he's dealt with really well.
"I think now is a good moment for him just to go home for a couple of days, clear his head. The pleasing thing for me is that we've got him back on the pitch.
"I think the fact that Raheem put out the tweet that he did the other night was real closure on that whole incident.
To all the @England fans, I wanted to leave things at it was but tonight I have to speak again : it was hard for me to see my team mate get booed for something that was my fault. Joe hasn’t done anything wrong & for me to see someone who keeps his head down and work hard..— Raheem Sterling (@sterling7) November 14, 2019
"We get Raheem back on the pitch [against Kosovo]. We won the match on Thursday and we can now just look forward."
England have already sealed Euro 2020 qualification leading into Sunday's final Group A fixture in Pristina.
Southgate will reportedly hand goalkeeper Nick Pope his first international start, while Callum Hudson-Odoi could replace Jadon Sancho in attack.