After a 6-0 thrashing by Chelsea and a 2-2 draw to Swansea, the Gunners fell behind to David Silva’s first-half goal at Emirates Stadium.
But the north Londoners battled hard and Mathieu Flamini’s second-half equaliser earned Arsene Wenger’s men a point.
You have seen this season that we can step up
And Szczesny was pleased with the resilience shown by his side against Manuel Pellegrini’s title chasers.
“We owe it to the manager, the fans and everyone at the club,” Szczesny told Arsenal’s website.
“Ourselves as well because you want to do yourselves proud as well. We lost 6-0 and that’s embarrassing for players who represent this club.
“We’ve not had a great time in the last couple of games but it’s all about responding well and that’s what we did. Of course it was difficult times but we knew if we stuck together and carried on working properly then a result would come.
“Hopefully, from now we can start getting wins. We didn’t get a win but it was a half-positive result and now we can kick on from that.”
The Poland international added: “We’ve still got a lot to play for. The FA Cup, we’re in a decent position – not as good a position as we’d like – in the league but we’ve got it all to play for so we’ll be on our toes and at our very best to go on and win all the games.
“You have seen this season that we can step up. We’ve been very unlucky with injuries.
“I think if you look at the players that have been out, it’s probably five or six players who are guaranteed in the starting line-up. We’ve been really unlucky.”
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