The Gunners went down 3-2 at the Liberty Stadium - their sixth defeat in 11 Premier League away games - to sit fifth in the table, four points off fourth-placed Chelsea.
But shot-stopper Szczesny believes the Gunners have enough quality to maintain their record of finishing in the top four in every season under Arsene Wenger and qualify for the Champions League once again.
He told London24: "I am confident we will get into the top four. We don't deserve to be outside the top four.
"We should be challenging for trophies every year and I believe the results will pick up and we will at least finish in the top four because we have the quality in the squad to succeed."
But the Polish ace admits the Gunners need to sort out their poor form on the road.
He added: "I have no idea why we can't win away from home. The results speak for themselves and we have been really poor away this season. I really can't explain it.
"We go everywhere and try to do our best but the results don't go our way. We have talked about it and cannot come up with an answer. We need to sort it out.
"We can't take many positives out of it (the Swansea match) because we lost the game and we are disappointed about it."