The Scot says the striker's injury is not a serious problem and that he missed the game at the Etihad Stadium as the club did not want to risk aggravating a groin problem
Van Persie was a surprise absentee for United ahead of their trip to the Etihad Stadium on Sunday, and Moyes' side missed their star striker as they lost 4-1 - their heaviest defeat at City for nine years.
However, Moyes revealed after the game that the 30-year-old had only been left out as a precaution after picking up the problem in training.
And the manager believes the ex-Arsenal man will be fit again sooner rather than later.
"I don't think it's that bad," the former Everton boss said. "We thought he was going to make it.
"He felt something in his groin, he did a little bit of training the past couple of days but he just felt it when he made any sharp movements and he didn't want to aggravate it so we took that decision."
Van Persie is United's top scorer in the Premier League this season with three goals in four appearances.