The Gunners kept their first clean sheet since December in the 1-0 win over Stoke to gain ground on Tottenham Hotspur and Everton in the race for a Champions League spot.
Szczesny believes that his defence dealt with the Potters' aerial threat decisively and wants a repeat performance against Sunderland next weekend.
He told the club's official website: "When Stoke come to the Emirates, you know they will play long ball and will not create a lot of chances. But it is all about winning the first and second balls at the back and we did that.
"It was vital for us to keep a clean sheet because we hadn't kept one for quite a few games. I am quite happy with it, and we didn't really concede many chances, which is a positive. I hope we can repeat that next week."