Mauro Zarate had Brum 2-0 ahead before Elano scored from the spot to give Manchester City a lifeline. A dubious penalty award for a foul by Sun Jihai on Gary McSheffrey resulted in the Blues midfielder settling the issue.
Erksson said: "I feel the referee got it completely wrong regarding Birmingham's penalty but before blaming the official, we should blame ourselves very much.
"If we want to talk about European football next season, we can't lose as many balls like we did today. Even when we were under no pressure, we gave the ball away.
"We should have done much better than that. If you concede two goals like we did, you will also never win a game in the Premier League.
"For Birmingham's first goal, we have a throw-in and 10 seconds later they have a man in behind us (Zarate) who scores.
"The second goal was crazy as well. They have a goal kick and three touches later they have scored.
"I thought our penalty was a harsh one and gave us a chance to get back in the game but that chance died when they scored their penalty."