The 22-year-old was sent off for Poland in the opening match of the European Championships against Greece and failed to win his place back before his team were eliminated in the group stage.
Szczesny has said that he has learned from a disappointing summer and is ready to show that for the Gunners this season.
He told the club's official website: "Obviously the sending off is part of] a learning curve for me and hopefully that will never happen again, but it has made me more mature.
"Before the game I had never felt better in my life. Physically I was really fit and mentally strong and it just shows you that you never know what is around the corner. In that way it made me more mature."
Arsenal continue their pre-season preparations with a friendly in Germany against FC Cologne on Sunday, August 12.