The Gunners ended a nine-year trophy drought by beating Hull City 3-2 after extra time in May and are now one of the favourites for the Premier League title after recruiting Alexis Sanchez, Mathieu Debuchy, Calum Chambers and David Ospina over the summer.
Arsene Wenger's side take on Crystal Palace at the Emirates Stadium on Saturday and the keeper is relaxed about the upcoming campaign.
"I don't think there's pressure at the moment. We took a lot of that pressure off by winning the FA Cup at the end of last season and had a very good game in the Community Shield against Man City," the Pole told reporters.
"I think we're enjoying our football and can't wait to get started.
"There's not too much pressure on winning the title yet; we're not thinking about that. We just want to kick off the season well and win the first game."