Van Persie, although not alone, was entirely ineffective during the 2-0 defeat at the Karaiskakis Stadium that put United on the brink of elimination from Europe's top club competition.
The striker, speaking to Dutch broadcasting channel NOS after the match, said his personal efforts on the night were hampered by some of his team-mates, who he felt were treading on his toes.
"Our fellow players are sometimes occupying the spaces I want to play in," he said after being whether he was allowed to drop deep to get the ball.
"And when I see that, it makes it difficult for me to come to those spaces as well. So that forces me to adjust my runs, based on the position of my fellow players.
"And, unfortunately, they are often playing in my zones. I think that's a shame."
The Dutchman did, however, admit he made mistakes himself, not least in the 82nd minute when Chris Smalling's cross found him in the box and he fashioned a shooting opportunity, only to blaze over the bar. It was United's best chance of the match by far.
Had his effort found the back of the net, David Moyes' side would have headed back to Manchester with a vital away goal under their belts, and the outlook would not have been quite as bleak.
"I rushed that shot," Van Persie said. "That's a shame because I don't get a lot of chances, so when you get one, you have to score."
The result has ramped up the pressure on Moyes, with United's manager admitting after the game it was the worst European performance had been "very poor".
But Van Persie insisted the woeful outing was just a blip and that United can still progress beyond the last-16 stage. The return leg is to be played at Old Trafford on March 19, when United will need to score at least twice if they are to have a chance of winning the tie.
"He [Moyes] is working hard at it, and so are we," Van Persie said. "Sometimes we play well, but not all the time. We don't have luck on our side. It's easy to point the finger at someone, but I'm not like that. We have to do better ourselves.
"With all due respect, we should be able to defeat this team 2-0 or 3-0," he added.