Lee Sinnott said he was convinced Pilkington had not played a back pass, adding: "Unless he has turned into Franz Beckenbauer.
"The only way Joe Anyon could keep it out of the net was to use his hands. The referee actually said 'why did he pick it up then?' It was bizarre."
The manager was unhappy with the performances of all four officials, but happier with his team's second-half display after a slow start.
He added: "For the first 15 or 20 minutes I thought Oldham started very well. I didn't think we were pressing as much as we could do.
"But after that we slowly warmed to it, most certainly in the second half where we got ourselves going. But you had a culmination there of, in my view, bad decision making, a bit of bad luck where we hit the post and cross bar, and then some wonderful saves from Mark Crossley."
Oldham boss John Sheridan said the back-pass decision was a pivotal moment.
He said: "It was never a back-pass, I couldn't believe he had given it. If their lad meant that he should be playing in the Premier. I think he went to clear it and it caught him and went back to the keeper.
"It changed the game because they were on top of us at that time.
"We got a break and I think that has won us the game."