Arsene Wenger's charges picked up their second piece of silverware in three months on Sunday, adding to their FA Cup success last season with a 3-0 win over reigning Premier League champions Manchester City in the Community Shield.
And the 24-year-old Szczesny feels Arsenal are capable of lifting their first title since 2004 next May.
"Looking at it on paper I think it is the strongest side we have had," the goalkeeper told reporters. "Except for obviously Thomas [Vermaelen, who has moved to Barcelona] we have not lost any key players.
"Even if someone did leave on a free contract [Bacary Sagna], we managed to replace them with good players.
"So we are looking stronger and stronger and we are very happy with that."
New arrivals Calum Chambers and Mathieu Debuchy were both impressive in Arsenal's victory over City, and Szczesny praised both players after they made their competitive debuts for the club.
"Calum is really solid, he is only 19 as well," the Poland international pointed out. "For him to make his debut for Arsenal at Wembley and do so well, that was very good to see.
"And Mathieu has a lot of experience so we hope to see him perform at that level all the time."