The scores remained level until the final 15 minutes of the contest at St Andrew's, when Ollie Watkins converted from the spot after Michael Morrison was judged to have brought down Neal Maupay in the box.
Maupay then went on to add a second in the dying minutes, condemning the Blues to their ninth league defeat of the season and leaving them teetering above the relegation zone.
"I have seen it back and I thought at the time it wasn't a penalty," Cotterill told reporters afterwards. "I thought Morrison got a toe to it, if you look at the direction of the ball to where their player is, he isn't going to take that touch because he isn't going to score from that angle. What's the point speaking to the officials? You only get into trouble, what's done is done, you can't do anything about that.
"They are a better footballing team but we knew that coming into the game because they have been doing it for years. I think up until the penalty, the efforts on goal would have been nip and tuck. They would have had a few more on target I would imagine. If you look at the first 30 minutes they didn't get into any rhythm, 30-40 minutes they had us on the ropes a little bit.
"I thought in the second half we were better than in the first half. The penalty has absolutely rocked us. I thought there was a lot of energy and emotion used in the game at the weekend and the penalty has killed us stone dead."
Next up for Birmingham is a trip to Barnsley on Saturday afternoon.