The Gunners are looking to end their nine-year trophy drought this season and face holders Wigan in the FA Cup semi-final on Saturday.
Arsenal were fancied against Birmingham in the 2011 League Cup final, but lost, a calamitous defensive mix-up between Szczesny and Laurent Koscielny handing the Blues victory.
"We had a bad experience recently at Wembley in the League Cup final," the goalkeeper told Arsenal Player.
"But (we've matured) a lot and we've got a lot more experienced players. Also I think that the likes of Jack (Wilshere) and Aaron Ramsey and myself were only 18 or 19 at the time.
"We're three years older now, we've got three years of experience under our belt and we're more prepared for it."
Szczesny accepts Arsenal are expected to end their search for a first trophy since the 2005 FA Cup this season.
He added: "It's huge - we know that we're in a very strong position to win the FA Cup this year, and we're two games away from doing so.
"We're at Wembley so we know how important it is for the fans and all the players.
"I hope it's going to be a very positive day for the club."