The Gunners suffered a new disappointment at the hands of Manchester United on Sunday, losing 2-1 to the champions at the Emirates.
Despite their eighth league defeat of the season, Szczesny feels that Champions League qualification is still a strong possibility.
The Polish international said: "We will win games, and will get our position in the Champions League.
"Obviously, I'm disappointed we lost but I'm not worried about the Champions League. I'm still confident we can do it."
Arsenal are currently one place outside of the Champions League qualifying positions in fifth.