The Gunners saw another campaign end without a trophy - the fifth in succession - as Arsene Wenger's men failed to last the distance both in the Premier League title race and Europe.
While some of that was down to the loss of key men like Van Persie and captain Cesc Fabregas - again linked with a move to Barcelona - at various stages to injury, on more than one occasion Arsenal also could not produce a big performance when it really mattered.
After overcoming defeats to Manchester United and Chelsea to force themselves back into contention, what would have been crucial points were thrown away at Birmingham, followed by away defeats at Tottenham and then Wigan - where they had led 2-0 with only 10 minutes left.
Van Persie - who returned to action at White Hart Lane in mid-April after some five months on the sidelines because of a serious knee injury - feels the Gunners need to make sure they can emulate the courageous effort shown in getting results at places like Stoke and Hull if they are to produce another serious title challenge.
"I just think we need to toughen up," the Dutchman declared.
"We need to make it clear to people: 'if you want to play football, we can play football. If you want to play hard, we can play hard.'
"We can do that, we have it within ourselves, but we need to do it consistently - because if we don't, we lose points and give the wrong message."
Wenger admits he will need to add a couple of players over the summer to help move the squad on to the next level.
Morocco striker Marouane Chamakh is to complete a free transfer from Bordeaux, while England keeper Robert Green, Fulham centre-half Brede Hangeland, Senegal international Pape Diakhate and Barcelona's defensive midfielder Yaya Toure are all reported targets.
Veteran former captain Sol Campbell - who led Arsenal through their unbeaten campaign of 2003/2004 - should provide some much-needed experience in the dressing room if a deal on a one-year contract extension can be agreed.
However, new deals for William Gallas and Mikael Silvestre are by no means certain to develop.
Nevertheless, Arsenal's rivals for Champions League qualification are all set to strengthen and Van Persie does not want Arsenal to be left behind.
"You can see the other teams are all improving," he said.
"We need some here and there too, we need a couple of players and we need to go ahead with that.
"You look at teams like Man City and Spurs - they are all coming up now.
"This year was an open league, but you never know what will happen next season.
"I think everyone realises that we need a bit of help in a few areas."
Fabregas, meanwhile, is set for another summer of transfer speculation following what the Spain midfielder claims was his best season for the Gunners.
The 22-year-old missed the end of the campaign after suffering a cracked bone in his leg during the Champions League quarter-final against Barcelona, which ruled him out of the return clash at the Nou Camp.
Fabregas, who played alongside Lionel Messi in the Barcelona youth ranks before moving to Arsenal in 2003, continues to find himself linked with a switch back to his former club, who are set to elect a new president on June 14.
Indeed, the player himself delivered something of a mixed message when speaking at an event in Spain yesterday.
However, Fabregas' parting message to the Arsenal supporters in his programme notes for the final Premier League match of the season against Fulham was of a positive outlook towards meeting the challenges for Wenger's young side next season.
"I think I have had many good years since I joined Arsenal, but in terms of personal performance, this has been the best," he said.
"Frustratingly, I think I could have done even better had injuries not struck."
The Arsenal captain added: "We have to make sure that those of us at the World Cup have good tournaments and come back happy, and that everyone else rests well - then we can all be on a good path to putting things right next season."