Gibbs returned from a six-week injury absence to help Arsenal become the first English team since Norwich in 1993 to win in Bayern's backyard.
But a 2-0 second leg victory could not prevent a third straight UEFA Champions League exit at the last-16 stage, and the sole focus for the season now is making up a five-point deficit on the Premier League's top four - starting at Swansea on Saturday.
Gibbs told the club's official website: "We are right to get criticism but we're not right to be told that we don't have character in the team.
"We showed that at Bayern, so anyone who has their doubts can have them - the belief is there in the team.
"We just have to turn that into results and correct our mistakes and things will look positive for the team.
"Munich's not an easy place to come and win the game, so we have to leave proud but disappointed.
"If we want to play in this competition again, we have to win on Saturday at Swansea and we have to win probably for the rest of the season. We have to forget about this now and focus on the Premier League."
Olivier Giroud, one of Arsenal's goalscorers in Germany, said: "This result is good for the future and we have to continue because we have a big game against Swansea.
"It will be a hard game but we need the win to reach Tottenham and Chelsea. We need to carry on."