Latics were sent tumbling out of the FA Trophy as they were beaten 2-1 at home by Hendon.
The Southern League Premier Division South visitors took the lead when Joe White slotted home from inside the box.
James Norwood equalised from the spot in stoppage time, but with a penalty shoot-out now looking likeliest, the Dons booked their place in the next round in the 96th minute when Niko Muir dramatically bundled the ball over the line.
Latics were dominant for large parts of the game, especially the earlier parts, but despite lots of shots, couldn’t make it count.
Disappointed Latics boss Micky Mellon said: "I'd have to apologise, I think, and it's the first time I've had to do that for a long time in my career.
"But I'd have to apologise on behalf of us as a management staff and a playing staff because with all due respect to Hendon, who came here and won and deservedly so, I think we all know that Oldham should be doing better.
"We have to be doing better than that."
Latics, who are sixth in the table, return to National League action on Tuesday night when they host Boreham Wood (7.45pm).
