Calvin Andrew’s 18th-minute goal put the visitors through, leaving Rovers manager Darren Ferguson to bemoan their lack of finishing power.
“I think there were a lot of good things about the performance, but it’s a cup match, it’s gone and we’re out. You don’t get it back and it’s a disappointing result,” said the manager.
“We threw everything we had at them in the second half, but we’ve only got ourselves to blame when you create that many chances and have a blank. That was the problem.”
Ferguson continued: “That’s two games on the bounce now where we’ve conceded a soft goal and while I can’t fault them for the chances they created I can fault them for not taking them.”
Only a top save from Josh Lillis kept Dale in front, as he brilliantly blocked Alfie Beestin’s effort from point-blank range before John Marquis hit a post in the 66th minute. The onslaught continued as Andy Butler headed wide, and Tommy Rowe missed another glaring opportunity when he blazed over from eight yards. Doncaster were also left furious after having several penalty claims turned down.
The visitors got what proved the winner and revenge for their recent 2-0 league defeat when Niall Mason conceded a free-kick and Joe Bunney’s delivery from the right was headed home at the back post by Andrew.
Doncaster Rovers: Lawlor, Blair, Butler, Baudry, Mason (Garrett 79), Houghton, Kongolo, Rowe, Beestin (Coppinger 64), Marquis, May (Mandeville 88). Unused substitutes: Alcock, Marosi, Wright, Ben Khemis.
Rochdale: Lillis, Daniels, McNulty, Ntlhe, Cannon (McGahey 90), Adshead (Keane 64), Henderson, Kitching, Bunney (Jordan Williams 69), Andrew, Done. Unused substitutes: Rathbone, Thompson, Inman, Moore.
Referee: A Woolmer (Northamptonshire).