"I saw loads of comments [about my future]," the striker told Sky Sports News. "I thought they would go away after one or two days but they didn't.
"I'm committed [to Arsenal]. This is my eighth year at the club so if you could name one player that is committed then it is me."
Reflecting on the three points that moved Arsenal into the top half of the Premier League table, Van Persie said: "It was a much-needed win.
"It was a great performance and we showed great character."
Van Persie's first goal of the afternoon, scored after 29 seconds, was Arsenal's fastest ever in the Premier League.