He then went on to win the Premier League the following season, finishing as the division's top goalscorer in the process.
Van Persie said to BBC Sport: "I get that the fans were angry with me.
"I was the captain, top scorer and we came third that year. But just sometimes you feel you need a challenge, a new adventure.
"If I hurt people, I'm sorry. But that's me. I made that decision and I stand by it. But that doesn't mean that I look in a negative way towards Arsenal."
Whilst the striker has fond memories of his time at Arsenal, he admits he has no regrets about the move.
"I cannot say one bad word about Arsenal Football Club - it is a beautiful football club, I had a fantastic time there," he added. "I arrived as a little boy, I left as an adult, as a mature player.
"At the crucial moments, you have to make tough decisions, and it was a very tough decision. But you have to stand behind them and this is what I did.
"I know if you make decisions like that, you're not going to please everyone. I learned quite a while ago that I will just be myself, I will make decisions about my life and I will accept them."