The Gunners ended their nine-year wait for silverware last month as they beat Hull at Wembley, with the Polish stopper paying a key role.
The 3-2 win proved to be Fabianski’s last outing for Arsene Wenger’s side with his contract due to expire in a few weeks’ time – he has since penned a pre-contract deal with Swansea.
The experienced glovesman believes that the success they achieved will could now start a new era of success at the Emirates Stadium:
“They are really close [to winning the title],” he told talkSPORT.
“What Arsenal were missing was that trophy to be honest. But with that we won this year it gives you the belief that this team is able to do big things.
“The other issue was we lost a few key players in the important part of the season.
“The bigger thing was to win the trophy though, so it gives you that extra belief that they can fight for the title next year.”
Arsene Wenger was under intense pressure heading into the FA Cup Final, but following the success he agreed to a new three-year contract with the north London club.