The Gunners currently occupy fourth spot in the Premier League, two points ahead of rivals Spurs, albeit having played a game more than Andre Villas-Boas’ side.
However, Szczesny is confident his side will end this season in the top four as they prepare to take on Wigan and Newcastle in their final two games of the campaign.
|7/2||Arsenal are 7/2 with BetVictor to finish the season as the top London club
"If you look at Chelsea's fixtures, they have Tottenham and Everton left and they won't be easy games. And Tottenham do not have enough quality, so there you go..."
Arsenal narrowly beat already-relegated QPR on Saturday courtesy of a single goal from Theo Walcott and Szczesny says winning is all that matters at this stage of the season.
"I would settle for another two 1-0 wins in the rest of the season and a place in the top three," he added.
"Even if we have games like the QPR one, it might have been boring at times, but we couldn't care less at this time. We just got the three points.
"Hopefully it will be back to the old days and hopefully we will get back to winning trophies as well."