The Gunners captain appeared to mouth "Oh no" when Wenger substituted Alex Oxlade-Chamberlain for Andrey Arshavin during Sunday's 2-1 loss to Manchester United.
"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," Van Persie wrote in a letter to The Sun.
"I was not questioning his judgment - 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 went on to praise the Frenchman, saying: "I have a lot of respect and admiration for Arsene Wenger.
"He is one of the best football coaches in the world, with a brilliant record of success here at Arsenal.
"I wouldn't be here or the player I am without him."
Van Persie insisted that there was no rift with his boss.
"The manager and I are fine and my relationship with the club is good," he said.
"There is no problem, there is no conflict and there is no controversy. The boss knows that, I know that, the players all know that.
"But it's important the Arsenal fans know that and that people in the game know that."
Sunday's defeat leaves Arsenal fifth in the Premier League with 36 points from 22 games.