Birmingham were awarded a last-minute penalty and, in protest at the decision, Gallas retreated to the halfway line and sat down sulking.
Gallas told L'Equipe Magazine: "The controversy about my captaincy? People had to find a scapegoat as we didn't win any trophies last season.
"So, they talked and talked again about the Birmingham match. Indeed I made a mistake. I must admit I flipped my lid. We should have won that game easily.
"There I became imbued with the winning culture, which doesn't exist yet at Arsenal.
"Of course, some of my Arsenal team-mates could not have appreciated my behaviour against Birmingham.
"I had to state my authority again and today when I motivate them before a match, they say; 'Capi, we need you, we are following you'.
"If I would have been an unworthy captain, they would have banned me.
"The critics went much too far. Maybe I put myself under too much pressure, like Arsene Wenger said.
"I believed I had a message to give to my team-mates and I could not find the right words.
"Our game made people dream, but we had empty hands. We have to show a more clinical state of mind. At the end of last season there was such a frustration inside me."