Sterling was stood down from the team to face Montenegro on Thursday after clashing with Gomez at the training ground following Liverpool's win over Manchester City on Sunday.
When the 22-year-old came off the bench during his country's 7-0 win over Montenegro, a section of the fans at Wembley booed him, much to his manager's chagrin.
"No, I don’t understand it. No England player should ever be booed," Southgate told Sky Sports.
"We’re a team, Joe has done nothing wrong, absolutely. I’ve made that clear earlier in the week, so I don’t understand that.
"Him and Raheem are very close and the whole team are very close so we don’t want to see anybody treated in that way."
Southgate: The whole dressing room 'disappointed' with Gomez boos
Southgate's words echo those of Sterling himself, who has also criticised the fans for their reaction to his international team-mate's arrival.