Birmingham went ahead through Nikola Zigic after 33 minutes as once again the Gunners - who lost two straight league games before the international break - failed to make the most of their early possession.
"Victory was imperative," said the Arsenal manager.
"We were backs to the wall in the championship, where we were in a position where we really had to win, and when we went 1-0 down, we made it even more difficult.
"We played with nerves, and you could see our fluency was affected by the fact we had not won for two games.
"We played a bit with the hand brake in the final third, especially when we were 2-1 up.
"It was never comfortable today, you could see and feel that in the way we played."