Gomez was jeered by home fans during the 7-0 win over Montenegro.
It came after Gomez was left with a scratch down his face and neck when Sterling accosted him at the start of England's training camp.
The City ace subsequently sat out the Montenegro thrashing that saw England qualify for Euro 2020 as punishment.
But after the game he tweeted: "To all the England fans, I wanted to leave things as 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, especially after a difficult week, for him to be booed when he came on tonight was wrong.
"I've taken full responsibility and accepted the consequence.
"I felt as though I had to say this, get home safe everyone."
Three Lions boss Gareth Southgate echoed the winger's sentiment when speaking to the media after the whistle.
He said: "I don't understand it because no England player should ever be booed.
"Joe has done nothing wrong, 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 that way."