Arsenal can secure their place in the top three with victory over City at Emirates Stadium tomorrow but will not be jumping for joy after seeing their title hopes blown away in the last week.
They were beaten at Tottenham but even a victory at Wigan - where they let a 2-0 lead slip to lose 3-2 - would have left them three points behind Chelsea going into the weekend.
And the fact the Gunners have now failed to win a trophy since the 2005 FA Cup is not lost on Wenger, who is set to strengthen the squad during the summer.
Morocco striker Marouane Chamakh is in line to finally arrive at Arsenal, on a free from Bordeaux and Arshavin believes that with a few additions, the Gunners can last the distance next season.
"We had hoped for more, so we can't be satisfied with third," the Russian said.
"I can only say that next season we must try to solve this problem. It exists, so therefore something must be done."
Saturday's match against City will see Emmanuel Adebayor return to Emirates Stadium for the first time since his controversial summer move, while Patrick Vieira could also play against his old team.
Wenger, meanwhile, is hoping Alex Song will be fit to play.
Song has not featured since before the second leg of the Champions League quarter-final against Barcelona after a scan revealed inflamed cartilage in his knee.
With Denilson also missing the trip to Wigan because of a groin problem, youngster Craig Eastmond played alongside Samir Nasri in the centre of a makeshift midfield missing captain Cesc Fabregas for the rest of the season.
"Maybe Song [could be off the injury list]," Wenger said. "He has a test on Friday and we will see. He is a question mark.
"Apart from that, nobody is back. Andrey Arshavin is out. Everyone else - [William] Gallas, Almunia, Denilson - is still out too."
Defenders Kieran Gibbs (foot) and Johan Djourou (knee) are approaching fitness after long-term injuries, however.
"Djourou has a little chance [to play again this season]," Wenger said, "but Gibbs will be very short."