Everton manager David Moyes told Gabriel Clarke his side should have progressed at the first time of asking, but was quick to praise Oldham.
Matt Smith popped up with a last-minute equaliser to force a replay at Goodison Park, meaning the teams will have to battle it out once again.
"I think we should have seen the game out, but credit to Oldham. They've done it to Forest, and they've done it to Liverpool, and they almost did it to us," Moyes explained.
"Their keeper came and jumped up with his arms up in the air, and I'm not sure he's able to do that. I think there was a foul in the first corner."