The Frenchman believes the 23-year-old is developing at a swift pace after overcoming a disappointing Euro 2012 campaign and regaining his place in the side from Lukasz Fabianski
The Poland international has been ever-present for the Gunners as they moved to the top of the Premier League table, and produced a fine performance in his nation's 2-0 defeat against England.
Wenger insists he was never interested in signing a new goalkeeper during the summer - despite bringing in Emiliano Viviano on loan - and always had faith in Szczesny, who he believes will continue to improve as he gains more experience.
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"People forget with Szczesny that, at 23 years old, it is like being 18 for an outfield player.
"At 23 he has played two [full] Premier League seasons, one where we finished third and last year when we made 73 points and finished fourth. You would think that he can only go up."
Last season, Szczesny was affected by a disappointing European Championship and was briefly displaced by Fabianski, but Wenger believes the Pole is full of confidence again after overcoming those setbacks.
"I think he questioned himself, especially after the European Championship in Poland where it was a massive disappointment for him [after he was sent off in the opening game] - I think it affected his belief," the Frenchman continued.
"He has matured through disappointments, like we all do. I believe every big player has to go through that in his career. And what may decide his career is how he comes out of that and I believe he came out in the way I wanted.
"It took him a while but he came back stronger. I took him out of the team last year and since he has come back into the team he has been consistent."