The Emirates Stadium outfit have won just two of their first seven Premier League matches this season, leaving them eighth in the table.
And although they have only lost once - Sunday's 2-0 reverse at Chelsea - Arsene Wenger's men are already nine points off the pace.
Arsenal have already played four of last season's top six, though, and Szczesny feels his side will hit their straps in the coming weeks.
"We have had a tough run so far," Szczesny is quoted as saying in the Express and Star.
"But I would like to think that our start has been solid. [It is] not as good as we expected from ourselves.
"But I believe that after the international break, we can push on and get more points."
Arsenal's Premier League campaign resumes with a home clash against Hull City on October 18.
