The Gunners have struggled in recent weeks after crashing out of both the Champions League and the FA Cup.
But Szczesny believes Arsenal can pip Manchester United for the Premier League title.
He said: “I don’t care what people say.
“The only way we can respond is by going out on the pitch and showing people what we are made of.
“We are confident we are a very good team and we believe we can win the league this season – that is the only way to shut them up really.
“We’re heartened by United losing their last two games. We’re going to try to take advantage of it.
“They’ve dropped points and we’re going to do our best to win all of our games coming up – then we’ve still got to play them at the Emirates.”