The north Londoners sealed victory over the Potters thanks to Lukas Podolski’s late deflected free-kick at Emirates Stadium.
And Szczesny felt the result was nothing less than Arsène Wenger’s men deserved.
“I thought we dominated the game from start to finish and deserved the victory,” he told Arsenal Player.
“Their goalkeeper, who has been outstanding this season, was man of the match and that shows the [scoreline] should have been higher. But we will take the victory and we’re happy with it.
“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.
“We dominated [Peter] Crouch and [Jon] Walters so they never got going. They never had a chance to get anywhere near me.”
The Gunners goalkeeper also revealed his delight at keeping a clean sheet, his first since the 1-0 win over Swansea in the FA Cup last month.
He added: “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.”