Robbie Blake gave Rovers a fourth-minute lead at Boundary Park on Saturday but Matt Derbyshire's brace proved decisive after Reece Wabara headed the hosts level.
Doncaster were badly hit by injury and suspension, with their list of absentees including David Cotterill, Iain Hume and Billy Paynter.
Saunders said: "We were missing a lot of our big players, but I still thought we had enough to go and win the game.
"It wasn't the team I would have liked to put out and you could see that some of our players' fitness was lacking in the second half. Four or five of them 'blew up', but it's still disappointing after the start we made.
"For the first 20 minutes we were brilliant and we had five or six chances - enough to kill off the game.
"It could have been over and we had Oldham on the floor, but we allowed them to get back up again.
"We let them come back into it and I'm not happy about the manner in which they scored their second and third goals.
"I'm disappointed because a cup run would have been great, but fair play to Oldham and good luck to them.
"We'll move forward from this and hopefully continue our good run in the league."