Arsenal were notorious for grinding out 1-0 victories during their heyday and Szczesny hopes the team's current form - they are unbeaten in nine - will be the start of something special for the club, who last won a trophy eight years ago.
"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."