Lions skipper Alan Dunne's 51st minute goal ensured that Ian Holloway's side secured all three points with a 1-0 victory, their first win at St Andrews since 1968.
"It was a frustrating night and a frustrating performance in many ways," Rowett said after the match.
"I felt when we went out from the start it felt a little bit flat and felt a little bit as though we were going to turn up and win the game.
"It just doesn't happen like that. I thought Millwall blocked the game up well and it was very difficult for us to find space and we just didn't move the ball quick enough and we didn't cause them enough problems in the final third and that was the most disappointing thing.
"Games like that are going to happen and we have to try and find a solution. It was a poor goal to concede and from then on we huffed and puffed.
"At the moment we seem to put in a good performance and then seem to be a bit flat the next time which can often come on a Tuesday night so soon after an way game on the Saturday. But we have to be better than that."