The 22-year-old Poland international has pledged his loyalty to the Gunners despite Lukasz Fabianski keeping two clean sheets in the last two games for the north Londoners.
Szczesny missed the games against Bayern Munich and Swansea because Arsenal manager Arsene Wenger felt he had been 'mentally affected' by the number of games played.
"I am too happy to go somewhere else. I believe in the philosophy of the club and that Arsenal will start to win again.
"I have a debt to pay here for the club, I owe them. I just do not want to go anywhere else. As long as they want me here, there is no 'somewhere else', and I have a contract until June 2015."
The weekend's results helped Arsenal's bid for a top four finish somewhat, with their 2-0 win at Swansea leaving them four points behind north London rivals Tottenham with a game in hand after Spurs slumped to a 1-0 home defeat at the hands of Fulham.
Szczesny feels it would be unthinkable if Arsenal were to miss out on Champions League football next season behind Spurs or Chelsea.
"It would be a disaster not to be in the top four and without Champions League next year. We have the 10 most important games in our careers. We are going through the most difficult time since I came here."
Arsenal's next league game sees them take on Reading on March 30, at which time they expect key player Jack Wilshere to return from an ankle problem after he missed the trip to Swansea.