The Gunners sealed their progression to the last 16 on Wednesday with a 2-0 win over Montpellier and face Olympiakos in Athens in their final game of the group in December.
And the 22-year-old has admitted that, while he wants to win the competition, he is hoping that a good run in Europe won’t hinder his side's domestic form.
“You only take part in competitions with ambitions to win it, don’t you?” Szczesny told the Evening Standard.
“There are other, fantastic teams in Europe who are more likely to win it. But I’m in this competition to win it.
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Despite being second in Group B behind Schalke, the Poland international isn’t fazed about facing a potential winner from another group in the knockout phase of the competition.
He continued: “It’s hard to say how vital it is to win the group. In the last 16, whether you come first or second, you come up against the best teams in Europe.
“We finished top of the group last season and played AC Milan away and lost 4-0 so I’m not sure if it’s the most important thing. Now we’re satisfied with qualifying.
“Arsenal have qualified for the final 16 every season for the last few years. I don’t think us qualifying is a surprise.
“Chelsea and Manchester City not doing it as well is a big surprise but at the moment we’re just enjoying getting through.
“You have ups and downs and we had a tough couple of weeks recently. But we came back stronger than ever against Tottenham.
“We want to enjoy that moment for as long as we can.”