The home side scored twice in each half and had a penalty saved while the match was goalless.
In quotes released on the team's Twitter feed, the Lions' manager said: "We knew Birmingham were a high-energy team and that we had to start quickly. But we didn't, and it was a very poor showing.
"I can accept losing a game if you have a real go at it but that wasn't the case tonight, and for that reason it was unacceptable.
"Saturday is a massive game ahead of the international break. You can't just turn it on when you want in the Championship."
The result leaves Millwall 16th in the table ahead of their game against Bournemouth this weekend.