The Gunners 2-1 home defeat by Aston Villa leaves them in real danger of being overtaken by FA Cup winners Manchester City in the race for automatic Champions League qualification.
Since suffering a dramatic last-minute defeat to Birmingham in the Carling Cup final at Wembley, Arsene Wenger's men have recorded just three wins in all competitions as swift exits from Europe to Barcelona and the FA Cup at Old Trafford followed before a total collapse of their Barclays Premier League title bid.
Hitting a wall: Robin van Persie is at a loss to explain Arsenal's recent woes
Van Persie - whose late consolation goal took his tally to 21 and was his sixth in the last seven games - accepts Arsenal need to show more courage if they are to turn potential into trophies.
'There were lots of things (which went wrong) - we were not consistent enough. It is difficult to talk about it now,' Van Persie told Arsenal TV Online.
'It is going to be difficult to finish third, but we still have one game and have to win that to at least give us a chance.
'Next season we have to try [to come back stronger]. Everyone starts from scratch and we have a chance, it is up to us to prove it.'
Head ache: Gunners boss Arsene Wenger couldn;t look as his side suffered a 2-1 defeat at home to Aston Villa
Thousands of Arsenal fans had already headed for the Emirates Stadium exits ahead of the squad's lap of appreciation, with boos greeting the final whistle.
Despite seeing victories over Barcelona, Chelsea and Manchester United this season, the fans - who next season face a 6.5 per cent hike in ticket prices - have been short-changed as once again a campaign which promised so much failed to deliver.
Wenger accepts the fans have the right to vent their frustrations.
Van Persie added: 'The supporters have been great, every single game they have been supporting us tremendously and I am really proud to be a Gunner with them as our fans.'
Positive thinking: Van Persie is confident Arsenal can get back on track to success next season
Should Manchester City beat defeated FA Cup finalists Stoke at Eastlands on Tuesday night, then Roberto Mancini's big-spending team would climb above Arsenal ahead of the final round of top-flight fixtures next Sunday.
Were Arsenal, who topped the table in late November, to finish fourth, they would face a qualifier to again play in the Champions League, which then means pre-season plans, expected to include a first tour to the Far East, would probably need to be adjusted.
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