The midfielder scored in the 3-2 shock.
"Everyone in the dressing room is completely devastated," Allen told the Liverpool Echo.
"It's the worst feeling in football. These are the kind of games where mentally you have to be on it for the whole game but we started slowly.
"To concede three goals in the manner we did was bitterly disappointing. We wanted to do well in the FA Cup but now we're out.
"I don't think we underestimated them. But, no disrespect to Oldham, when you've been knocked out by a team in League One then something has definitely gone wrong somewhere.
"It hurts and I feel sorry for the fans. When you are representing Liverpool, you represent them. Once again they turned up in their thousands and they have gone home very disappointed."