Arsenal spent large parts of the season on top of the Premier League but they were unable to convert that into a title win as Manchester City finished the campaign at the top.
They did manage to end their nine-year wait for silverware, though, with the FA Cup and Szczesny believes there is plenty to be positive about at the Emirates Stadium.
"We've been fighting and not a lot of people believed in us at the start of the season," the goalkeeper told the club's official website.
"But we stuck together and played very well for most of the season.
"I think the character is one thing you cannot question with this team. We dropped out of the title race but I think mentally we showed some great strengths.
"I think the most positive thing is that there's a lot of improvement and there is still a lot of room for improvement."
Szczesny played in 37 matches for Arsenal last season, keeping 16 clean sheets along the way.
