An uninspiring 0-0 draw with Manchester United followed Arsenal's 5-1 hammering at the hands of Liverpool at the weekend - results that have seen Chelsea leapfrog the Gunners to go top of the Premier League table.
However, despite a difficult week at the Emirates, Szczesny believes his side are still very much in the hunt.
"We have dropped points in our last two games and now we have a lot of teams very close together at the top," Szczesny told the Sun.
"It is going to be tight but we will put everything into our last 12 games of the season and if we show our character I believe we can do it.
"We will be fighting right to the end and that's the least you can expect from players playing for Arsenal Football Club.
"We showed a lot of mental strength to recover from the weekend defeat at Liverpool and now it's time for us to push on and give it a real go.
"We are a bit disappointed that we didn't beat Manchester United on Wednesday but at least we got a point against a very good side and the clean sheet is also a positive."
The Polish stopper has been in fine form this campaign, and has been an integral part of Arsenal's improvement.
He is especially difficult to beat at home, having not conceded at the Emirates since early Demember, and he had to be at his best to preserve that record against United, producing a stunning save to deny ex-Gunners hitman Robin van Persie late on.
"Robin has not scored a lot of headers at the Emirates and I wanted to make sure he did not score the first goal," Szczesny added.
"It was a good save but I am disappointed because it did not give us the win."