The Gunners came from behind to beat Crystal Palace 2-1 at the Emirates Stadium on Saturday thanks to a dramatic stoppage-time winner from Aaron Ramsey.
Although Arsenal looked sharp in attack throughout the match, the home side were undone by some slack defending which allowed Brede Hangeland to head Palace in front from a corner.
Arsene Wenger's side managed to level before half-time through Laurent Koscielny, and Arsenal's pressure paid off after the visitors were reduced to 10 men when winger Jason Puncheon receieved a second yellow card.
"Maybe it was not the most beautiful of games, going 1-0 down we had to respond, but we will take the three points," Szczesny said.
"We conceded to another set-piece which was not very good, although it was a good delivery and a great header, so that is something we can hopefully improve on."
Meanwhile, Szczesny is confident Arsenal can get a positive result at the Ataturk Olympic Stadium when they play the first leg of their Champions League qualifier against Besiktas on Wednesday.
Arsenal won 3-0 against Fenerbahce in Istanbul at the same stage of the competition last season, and the Poland international reckons that experience will prove vital.
"We love important games, so we can't wait to go to Turkey. It will be a good atmosphere," Szczesny said.
"We did really well in Istanbul last season, so will be out to do the same thing over again.
"The crowd is fantastic for the home team but they were out there last year too, so hopefully we can do it again."