United's season went from bad to worse on Tuesday when they went down 2-0 to Greek champions Olympiacos in the first leg of their Champions League last-16 clash.
Moyes shouldered the blame for the damaging defeat in a competition that represents United's last chance of silverware this season.
United are 11 points adrift of the top four and Moyes is coming under increased pressure, but van Persie backed his boss.
"He is new and needs time. He's working hard and so are we," van Persie is quoted by The Sun.
"It's easy to point at the manager but that's not who I am. We need to do it on the pitch."
But the former Arsenal man refused to pull any punches on their current plight.
"We are lousy - in a lousy position in the league, out of the cups and this looks a difficult one also," he said.
"We are very disappointed. It's a tough season.
"Sometimes we play good but not always. And we are not lucky. That's no excuse, though. We need to turn it around.
"We are able to play in a high tempo with massive power but in Greece it was all too slow.
"Olympiacos didn't create a lot either. The first goal was lucky, the second goal was a great one and for the rest of the game they didn't have any good chances."
Van Persie insists that United can still go through.
"It is possible to beat them at home with 2-0 or 3-0, but it won't be easy," he said.