Slack defending allowed Ched Evans and Harry Souttar to capitalise from set pieces before Niall Ennis grabbed a consolation effort for Rovers.
Doncaster chief Darren Moore felt his side deserved more.
“We’re the away team and I’m the away manager and I’m saying I’m disappointed that we have lost.
“At worst, it was about coming away with a point but we went out to win the game.
“We thought it was going to be tight but we thought there would be space in between them, which there was.
“We went round them and on the outside of them but when we got around the box we just didn’t get the final touch.
“They got two goals from set plays. Up to half-an-hour in, we were not in any danger and felt comfortable.
“I’m disappointed because we’ve let three points go but we move on to the next one on Tuesday.”
Moore said he was largely pleased with the performance of his side but bemoaned a lack of a killer touch in the final third.
“I’m not going to cry over spilt milk because I saw enough signs from us and we’ve come a long way. I did see a resoluteness and solidness to be the away team and that’s what we need.
“We need to make sure we’re building on performances like that.
“We just need a bit more craft and guile in the final third.”
Fleetwood Town: Cairns, Coyle (Madden 71), Connolly, Souttar, Gibson, Andrew, Burns, Whelan, Sowerby, Josh Morris (Coutts 62), Evans (Saunders 90). Unused substitutes: Baggley, Crellin, Hill, Garner.
Doncaster Rovers: Dieng, Halliday, Wright, Anderson, John, Whiteman, Sheaf (Coppinger 73), Taylor (Okenabirhie 81), Gomes, Sadlier (Cole 68), Ennis. Unused substitutes: Ramsey, Reece James, Jones, Blair.
Referee: R Joyce (Cleveland).