Dutch striker Van Persie, who scored Arsenal's equaliser, appeared to voice his disapproval when Wenger substituted Alex Oxlade-Chamberlain for Andrei Arshavin - a decision that also prompted a chorus of boos from the crowd.
"The manager and I are fine and my relationship with the club is good," said Van Persie, whose 19 league goals have been the silver lining in a poor season for Arsenal so far.
"There is no problem. There is no conflict, and no controversy. I was not having a go at the boss on Sunday - I was just sad to see Alex leave the pitch as he just gave the assist for our only goal.
"I was not questioning Wenger's judgement - I know it's not my place to challenge what Arsene Wenger does. He is the boss, he makes the decisions and that's it... end of story."
Van Persie said he did not realise teenager Oxlade-Chamberlain, whose pass set up the goal, had been carrying a calf injury prior to Wenger switching him.
"We did not know but the boss did and brought Andrei Arshavin on."
Despite losing their eighth game of the season and trailing fourth-placed Chelsea by five points, Van Persie said it was not all doom and gloom at Arsenal and that they can still secure a top-four finish.
"Losing to Manchester United was a setback, but it was not a knockout blow," he said. "Anybody writing us off is making a mistake. This could still be a good season for us. We have the FA Cup to look forward to and the Champions League."
Arsenal face AC Milan in the last 16 of the Champions League.
'When PSG went 1-0 up against Liverpool, all of a sudden I started getting abused. At the end of the game, I felt like I grew 10 feet walking around Anfield!': Manchester United legend reveals sitting in home end of Champions League clash
'It’s unacceptable for Arsenal to be making the same mistakes year-after-year with the same manager': Gunners legend makes huge Mikel Arteta claim after Premier League failings
