After captaining the Gunners to their FA Cup victory over Plymouth Argyle, Van Persie said: "When I arrived at Arsenal they were winning trophies for fun.
"They were champions when I arrived and in my first season we won the FA Cup. I was expecting that to carry on but it hasn't really happened like that. We need to win a trophy as soon as possible. If we can win something this year it will be a big, big achievement."
Van Persie has his heart set on a first trip to Wembley with Arsenal, although he was forced to admit: "I still can't guarantee that it will happen this season.
"We're improving day by day but we're not there yet. Everyone still needs to improve. Sometimes you have to win ugly to achieve something."