However, Gibbs was pleased with how his side performed in Munich, and he has admitted that they now need to take that form into the Premier League as they attempt to secure a place in the top four.
The 23-year-old 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."
Gibbs has featured 26 times for Arsenal this season.