Arsene Wenger’s men were in contention for four trophies in February but crashed out of three competitions in the space of two weeks.
Their shock Carling Cup final defeat to Birmingham was followed swiftly by a Champions League exit at the hands of Barcelona and an FA Cup quarter-final loss against Manchester United.
The Gunners remain in contention for the Barclays Premier League title but are five points adrift of United with a match in hand.
Their fate remains in their own hands with the leaders still to visit Emirates Stadium but Van Persie accepts they have to learn the lessons of their previous disappointments to end the club’s six-year trophy drought.
“We always do our best at Arsenal and always want to win,” the Holland international said.
“On a number of occasions we have been very close but, at the last moment, it’s often not good enough. That’s the reality.
“It’s very frustrating when you lose, especially as a team when we’re so close. But we have to look forward and now it’s up to us to change all that.
“I firmly believe in the team, Arsenal and myself and I’m positive we will win prizes.”
Van Persie has rejected suggestions that he could consider moving away from Emirates Stadium in a bid to secure more honours.
He added: “Absolutely not. I’m happy here, I have a contract with Arsenal and I fully respect that.”