Arsene Wenger's men are painfully aware that their club has not won a trophy for six years.
Szczesny said: "We're still confident we can win the league."
The Polish goalkeeper, who is out for a month with a finger injury, added: "I don't care what people say.
"Manchester United have dropped points, but if we get the right results and we beat United at home, we're going to win the league. Simple."