Ther home side also had to play the whole of the second period with just ten men after Lee Carsley was shown a straight red card for a bad tackle on Chris Iwelumo on 37 minutes.
"We didn't deserve much more than we got to be quite honest," the Wolves boss told Sky Sports.
"I'm disappointed with both goals. Both mistakes. The first one certainly, it was abysmal defending by us.
"We haven't done ourselves any good in terms of defending there.
"There's lots of things I'm not happy about, decisions prior to it, but I end up moaning about it don't I, so our part in it was the biggest bit that cost us.
"I didn't want Carsley to go off. It's not ruined the game for Birmingham, it's ruined it for us. After that there weren't too many decisions we got.
"Having scored the goal when they did they were allowed to sit back.
"it was a poor, poor game for us."