United lie seventh in the Premier League, having displayed inconsistent form in Moyes' first season in charge since taking over from Alex Ferguson.
The absence of Van Persie, who has been out for a month with a thigh problem, has not helped the Old Trafford club's cause.
However, the Netherlands international is confident the reigning champions will soon improve and believes supporters must be patient with Moyes.
In quotes reported by the BBC, Van Persie said: "Moyes needs time; he's new.
"The manager is our leading man and he will change things around.
"We lost too many points this year, but we are doing everything we can to change that."
Moyes has yet to win a top-level trophy as a manager, and Van Persie acknowledged there was little celebration in the United ranks when the club marked the start of the Scot's reign by claiming the Community Shield in August.
"We are used to winning," the forward added. "If you win a game, it's a normal day at the office.
"After the Community Shield win, none of the players really celebrated, or played music, as it was the way things were."
