The Netherlands international missed the 4-1 derby defeat to Manchester City on Sunday with a groin injury.
Moyes confirmed that Van Persie is unlikely to play a part at Old Trafford in the third-round tie but could return for Saturday's Premier League game against West Brom.
"I don't think Robin will play on Wednesday. But I think he'll have an outside chance for Saturday," Moyes said on Tuesday, before explaining how his side are looking to move on from their humbling at the Etihad Stadium.
"It's gone now isn't it? I can't do anything about it so we move on and get ready for the next game.
"It did (shock me). But when you're a football manager for the length of time I have been, you are always going to have shocks. I've had lots and I have got no doubt there will be more in the future. That's the way football is."
Luis Suarez is in line for a return to the Liverpool fold on Wednesday after serving a 10-game ban for biting Chelsea's Branislav Ivanovic in April.
Moyes believes that clashes between the two sides are always significant, regardless of Suarez's potential return.
"When you play Liverpool at Manchester United, it's a big rivalry," he continued.
"It could take on a bigger significance than maybe people would expect.
"It's an important game for us. We want to try and do well in all the cup competitions and that is what we will try to do.
"It (Suarez's return) means that Liverpool have got a really good player. So, does it change the complexion (of the game)? I don't know. I'm not looking at Liverpool too much but the qualities of Luis Suarez are very good."
Moyes also refused to comment on assertions by Real Madrid president Florentino Perez that United had made a bid for Gareth Bale, prior to the winger joining the La Liga side.
"If we did make a bid I wouldn't tell you," he said. "We don't talk about players. I would not comment on that."
