Substitute David Syers headed home in injury time as Rovers stepped up their bid for promotion from npower League One.
The visitors had taken a third-minute lead when Billy Paynter's effort came back off the post and defender Rob Jones headed in the rebound from eight yards.
Oldham then took control and made several chances before levelling after 27 minutes, Youssouff M'Changama's 25-yard drive flying through the grasp of Rovers goalkeeper Gary Woods.
The busy Woods made a fine save to deny Jean Yves Mvoto and, in a close-fought second half, both sides were on course for a point, but Rovers left-back Tommy Spurr swung in a deep 91st-minute cross and Syers headed past Oldham goalkeeper Dean Bouzanis from close range.
Dickov said: "Doncaster are one of the best teams in this league and we more than matched them. Over 90 minutes we deserved at least a draw. We'll be fine if we keep performing like that.
"The fans' reaction tells you a lot and we've been clapped off the pitch even though we lost 2-1. We had 11 shots to Doncaster's four and there were times in the first half when we were excellent.
"To concede so early was obviously poor, but we reacted really well and were a bit disappointed to come in level at half-time. The players did ever so well, but we made a mistake with a couple of minutes left and their second goal was a sickener.
"It came down to game management because we left ourselves open with our over-eagerness to get players into their box.
"Teams will pick you off when you make that sort of mistake, so it's very disappointing to get nothing when we didn't deserve to lose."
- Sports & Recreation
- David Syers
- Gary Woods
- Billy Paynter