The Gunners still have some work to do over the final three games of the Premier League to make sure of third place ahead of Newcastle, starting at Stoke this weekend.
Nevertheless, just to be in this position is an achievement in itself given the appalling start to the campaign, which saw Arsene Wenger's men slump as low as 17th after four defeats in the opening seven matches.
The Gunners put together a run of seven straight wins to drag themselves back up into the top four, and Szczesny accepts it will take similar performances on a weekly basis if Arsenal are to match the achievements of Chelsea by reaching the Champions League final again and also mount a sustained assault on the domestic title.
"I think the quality is there. We all know it - we have the quality to fight for trophies in Europe and this country," the Poland goalkeeper said.
"It is just consistency that has been a bit of a problem for us this year. But the team is getting more experienced and hopefully we have got the experience to win trophies next year."