The Polish shot-stopper believes the Gunners deserve some silverware and is hoping they can pick up nine points from their remaining three fixtures to ensure a third place finish
The Gunners last tasted success in the 2005 FA Cup with a win over Manchester United but Szczesny believes the Gunners are in good shape to break that run next season.
“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.
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“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.”
The north London side suffered a difficult start to their Premier League campaign, slipping as low as 17th following heavy defeats to Blackburn Rovers and Manchester United.
However, Wenger’s men produced a stunning second half to the season and now look in good shape to finish third in the league.
But Szczesny is not taking anything for granted and says he hopes the club can sign off for the season with three wins from their final three games.
He continued: “I think if you look over the last couple of months we're probably one of the best teams in the Premier League. So we've got three games to go and we need to win all three and we'll finish third.”