The Gunners have not been victorious since they lifted the FA Cup in 2005.
However, Szczesny is adamant that the squad is now experienced enough to end their seven-year wait for a trophy.
"When you play for this club you want to win trophies," he told reporters. "This club deserves trophies and we didn't get any this year so it's always disappointing.
"I think the quality is there. We all know it. We have the quality to fight for trophies in Europe and this country. It's just consistency that has been a bit of a problem for us this year.
"But the team's getting more experienced and hopefully we've got the experience to win trophies next year."
Arsenal are currently third in the Premier League table.