Victory at Boundary Park would have put Dons in the automatic promotion places but they were outplayed and undone by goals from Shefki Kuqi and Tom Adeyemi.
Robinson said: "I am devastated by what happened tonight. We didn't turn up and the performance was not good enough."
He added: "Conditions were difficult but it was exactly the same for both teams and nobody can use that as an excuse.
"We were poor in a number of ways so we have to learn from that and compete far better as a team. We win together and we lose together but not many of the players have come out of this with any credit."
Oldham boss Paul Dickov was delighted with the result and the performance of his players, and said: "It is pleasing to get a home win because everyone has been reminding me about our record here and I want home form to be very strong.
"I'm delighted to beat one of the best teams in the division and to do it playing really good football.
"It got a bit hairy towards the end but for 80 minutes we were excellent both with the ball and without it.
"We set ourselves up very well as a team and created lots of chances.
"There were good performances right through the side with the likes of Tom Adeyemi, Chris Taylor and David Mellor, who was fantastic at left back for a young boy up against good players."