The Brewers made hard work for themselves, going two-nil up with 25 minutes gone before relinquishing the lead.
Peter Cavanagh's unstoppable volley got Rochdale back into it after 43 minutes before Nathan Stanton's poor back pass let in Bobby Grant to make it 2-2 after 54 minutes.
However, Calvin Zola's neat control and cross from the right enabled Billy Kee to dive and chest home Burton's third goal - and his second - for the winner.
Dale had ended a four-game losing streak with a 4-1 win over Cheltenham on Friday but this clash reminded Coleman that his side have not turned things around yet.
"The game could have gone either way but, in the end, we got stretched when we were chasing the game and they had chances," Coleman said.
"We've conceded soft goals again and we're going two down far too often - we can't keep doing that.
"We were better in the second half but we can't compete if we keep on conceding goals like that.
"We can't always score four goals to win a game, even though we look capable of scoring them.
"We had a big following of fans who were superb in the way they got behind us, but we didn't respond well enough to it."
