Sterling had been dropped from the squad following an altercation with the defender at England's training ground following Liverpool's 3-1 defeat of Manchester City at the weekend.
Gomez faced a chorus of boos after coming on as a second-half substitute, with Sterling tweeting after the game to condemn the fans' actions.
Southgate: The whole dressing room 'disappointed' with Gomez boos
"To all England fans, I wanted to leave things as it was tonight but I have to speak again: it was hard for me to see my team mate get booed for something that was my fault," he wrote.
"Joe (Gomez) hasn't done anything wrong and for me to see someone who keeps his head down and work hard, especially after a difficult week for him to be booed when he came on tonight was wrong.
Abraham: 'Unacceptable' for England fans to boo Gomez
"I've taken full responsibility and accepted the consequence. I felt as though I had to say this."
England captain Harry Kane scored a hat-trick against Montenegro and says the decision to omit Sterling from the squad was a group decision.
"We made the decision as a group," said Kane. "The gaffer spoke to me and few of the other senior players in the team and this is the decision we’ve come to.
"Raheem’s apologised as we know, and for us, we’re a group, things happen, we move on and this was a great way to show it."