The Poland international is confident his side will win its last two games of the season and feels rival Spurs will drop points as the clubs battle to finish in the UCL places.
The Gunners currently occupy fourth spot in the Premier League, two points ahead of rival Tottenham, albeit having played a game more than Andre Villas-Boas’ side. Szczesny is confident his side will end this season in the top four as it prepares to take on Wigan and Newcastle in their final two games of the campaign.
"If we win our next two games it will be enough, because either Chelsea or Spurs will drop points because they play each other,” Szczesny told Arsenal Player. "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 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," Szczesny said.
"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."