Jon Otsemobor equalised for the Dons but Robinson's men conceded goals either side of half-time to go down 3-1 at Boundary Park.
"This is the first time I've ever said sorry to the chairman for the way we played," said Robinson, whose side now languish in the bottom half of League One.
"I would also like to apologise to the fans because that performance was just not acceptable.
"I have told the players exactly what went wrong, but anybody could have walked into the game and seen we weren't good enough.
"I can't defend that performance and I'm not going to try.
"Oldham worked harder than us and it's time for the players to stand up and be counted.
"There's playing football and there's being stupid and, for Oldham's first goal, we lost the ball just outside our own box.
"For their second goal we gave the biggest man on the pitch a free run at the ball. It's not good enough."