Szczesny produced an impressive display at Wembley on Tuesday night when he stood in for the injured Artur Boruc, despite being beaten twice as England secured a 2-0 victory which clinched their place at the 2014 World Cup.
The 23-year-old has never been short on confidence, but went through a difficult spell last season which saw him dropped for the Champions League tie at Bayern Munich and benched in favour of compatriot Lukasz Fabianski before eventually being recalled over the run-in.
It was a move which incurred the wrath of Szczesny's father Maciej, himself a former Poland international goalkeeper, who claimed his son was being made a 'scapegoat' for the team's shortcomings - and subsequently resulted in a public apology from the Arsenal player to Wenger and the club.
Wenger, though, maintains he never lost sight of Szczesny's long-term position, having seen the goalkeeper progress after joining the club's academy from hometown side Legia Warsaw in 2006 and a loan spell at Brentford.
"I was always convinced that Szczesny was make it," the Arsenal manager said.
"I didn't see the game on Tuesday because I watched the French game. I just saw (updates on my phone) every two minutes that Szczesny had made another save, so he was very good.
"People forget that at 23, it is like being 18 for an outfield player. At 23, Szczesny had played two Premier League seasons, one where we finished third and last year where we made 73 points and finished fourth. You would think he can only go up."
Szczesny's appearance at Wembley was only his second for Poland since being sent off in the opening match of Euro 2012, when he then lost his place to Przemyslaw Tyton.
Wenger, though, feels the way the goalkeeper has recovered his form for both club and country is confirmation of his character, which was tested soon after his arrival at Arsenal following five months out after fracturing both his forearms when lifting weights.
"I think he questioned himself, especially after the European Championships in Poland where it was a massive disappointment for him and I think it affected his belief. He matured through disappointments like we all do," Wenger added.
"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.
"For me, he came out of it 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 when he came back in the team since he has been consistent."
Wenger has no problems with Szczesny's "extrovert" personality, so long as that is translated through to strong performances between the posts.
"He was a bit kamikaze when he played at youth level, but he also made impressive saves," the French coach said.
"When you are young, you always think that life is easier than it really is. You discover by maturing that this level demands a daily attitude which is top level.
"Szczesny is an extrovert, who likes to be funny and all that. He is as well a happy boy, which is good.
"Sometimes these types of people will get the reputation of not being serious, but I think he is extremely serious in the way he approaches his job."
Wenger continued: "Self belief is always very important because self belief is linked to self esteem and in our job your self esteem has to be very resistant because football has strong emotions.
"For goalkeeper it is even more important because when you make a mistake you have the whole country on your back, so you have to be very strong on that front."