Blues winger Sebastian Larsson's goal cancelled out Steven Fletcher's penalty before Craig Gardner was shwon a red card for simulation.
McCarthy said: "Our position overall has deteriorated because there is a game less to go. That is blatantly obvious.
"It is a missed opportunity against 10 men but they have stuck at it and not given us too many chances.
"I think Birmingham are pretty adept at having two banks of four and making it hard for you to play against. We didn't have what was necessary to break the 10 men down unfortunately."