The Gunners endured a costly week in terms of their title challenge, following up the Chelsea hammering with a gutting draw against Swansea City that saw Mathieu Flamini score an own goal in the closing stages.
However, Szczesny believes that the draw against City will help his side to make a strong finish to the season, which could see them end their nine-year trophy drought as an FA Cup semi-final against holders Wigan Athletic awaits next month.
"We have not had a great time in the last couple of games, but it is all about responding well and that is what we did. Of course it was difficult times, but we knew if we stuck together, carried on working properly then a result would come. Hopefully now we can kick on," Szczesny is quoted as saying by PA.
"We owed it to the manager, the fans and everyone at the club, ourselves as well. We lost 6-0 and that is embarrassing for players who represent this club. You want to prove to yourself and prove to everyone around you that you are better than that.
"We have still got a lot to play for, the FA Cup and we are in a decent position in the league, so we will be on our toes and at our very best to go on and win all the games. I am confident we can have a very good run-in and finish strong."
Arsenal are now seven points behind league leaders Liverpool and just four clear of fifth-placed Everton, having played a game more than the Toffees.