United are facing the prospect of missing out on the Champions League - and the Premier League title looks beyond them already as they are 11 points behind leaders Arsenal, as well as being out of the FA Cup.
The club's struggles to maintain the level of the Sir Alex Ferguson years has been mirrored by a drop in the value of the club's shares on the New York Stock Exchange.
The shares hit 14.75 US dollars early on Thursday, the lowest point of the last 12 months, before then recovering to 15.16 dollars. It means the paper value of the club has declined by more than £250million compared to last May.
However, Holland striker Van Persie is certain that, given time, Moyes will succeed.
He said on www.guardian.co.uk: "I think he needs time like everyone, especially if you are new at such a big club.
"And to be fair, I don't think people don't understand that they have to give him a little bit more time, and I am talking about fans or even us. He will get that time and everyone is convinced that we will change things sooner than later."
He added: "We lost many points this season, too many in our opinion, because if you want to go for all the trophies, you have to play better and get more wins in - but we are doing everything we can to change that.
"The manager is our leading man in that case and he is trying his best and I think he will turn things around."
In a separate interview with uefa.com, Van Persie said his partnership with Wayne Rooney is going from strength to strength despite the strikers favouring the same position.
He said: "We realise that we are stronger when we are playing together, as a partnership.
"You are always stronger, in any sport, in life, when you are doing stuff together. With a player of Wayne's calibre, we can go from strength to strength, and we can become even better. One game he will score a couple, the next game I will score a couple. It is important that this partnership is becoming even stronger."
He added: "In a way we are both 'nine-and-a-halves', because we can play high up front and we can drop. That is an extra quality we have, which is quite rare.
"If you look around you have loads of main strikers, target men, foxes-in-the-boxes, and you have number 10s who are dropping in more.
"With us it's not obvious because we can both do that job. Wayne is doing a bit more, because he is playing behind me, but we can both do it."