Burton manager Paul Peschisolido was disappointed in his side's performance and conceded that Bury were worthy winners.
The Shakers claimed a 3-1 away victory following goals from Mike Jones, Nicholas Ajose and Efetobore Sodje with James Collins' first-half equaliser proving to be a mere consolation.
"They worked harder than us, they closed us down and we didn't pass the ball well. That was a recipe for disaster. It's disappointing after we've put in three fantastic performances to come up as short as we did," Peschisolido said.
"I don't want to take anything away from Bury because they're an excellent side who play nice football and deserved to win.
"We got ourselves back in it with the equaliser but I don't think we should have. I didn't think we were very good and we certainly didn't create many chances.
"I thought we could regroup at half-time and get the lads fired up, but we came out flat."