The loss left the Brewers without a win in their last three games. They are now fifth in the table, six points below third-placed Chesterfield.
"This was a match we could and should have won," Rowett told reporters. "The first half was probably the best we have played, the only disappointment was that we did not exploit some of the positions we got into.
"But in the second half for some reason we started to concede ground. Scunthorpe's goal was a good strike, but it was a disappointing one to concede from our point of view.
"From then on we were chasing the game but never quite got far enough up the pitch to do that. It's the first time I have lost my rag a little with the players after the game. I'm getting a bit fed up of hearing about unlucky Burton. I don't want us to be that. Football is all about going out and winning games, we have to have the nous to go on and win games like this."
Next up for Burton is a home game against Wycombe Wanderers on Tuesday evening.