"I feel the same as the fans, I want it as badly as them and it can be frustrating when it doesn't happen," said Van Persie, who has hit five goals in his last seven games.
"I am a positive person though, and I think positively, and I think the fans should do that as well.
"We did not win everything in the past couple of years, but we are doing absolutely everything we can to change it."
Van Persie added in the Arsenal matchday programme: "The main thing [in 2009] is to finally get silverware, but there is a clear picture here of how to achieve that.
"Things take time, and you often see clubs sacking managers for fun, and they don't get anywhere. You need a long-term strategy.
"At Arsenal, the players have time to grow into the system, and if we stick to our principles we will get silverware."