United's season went from bad to worse on Tuesday when they went down 2-0 to Greek champions Olympiakos in the last 16 of the Champions League.
Moyes shouldered the blame afterwards for their reversal in Athens, but with this being United's last chance of silverware this term - the loss still came as a major blow to the club.
Given United are currently 11 points off a top-four finish, it has been suggested Moyes is under pressure at Old Trafford - but the Dutchman 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.
"Olympiakos 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 against Olympiakos, but concedes things won't be easy.
"It is possible to beat them at home with 2-0 or 3-0, but it won't be easy," he concluded.
It was a frustrating night for the Dutchman as he struggled to make an impact in Greece, but he claimed after the match that his cause was not helped by the positioning of some of his team-mates.
"It was quite difficult because my team-mates are often in the area where I want to play," he said.
"That's why I have to change my tactics. Unfortunately, they are often in my area.
"It was much too slow and we only had one shot on target in the whole match against Olympiakos, which is far too little. Everyone is very disappointed."