The Gunners ended their 10-year wait for silverware by beating Hull City in the FA Cup final at Wembley in May.
The defender told the club's website: "Once you've got one [trophy], [you] want to experience it again. Everyone was over the moon with winning The FA Cup, it was such a big thing for us all.
"Fingers crossed we can compete on all fronts this season. We have the squad and we are signing players like [new signing Alexis] Sanchez, so I don't see why we can't."
Arsenal have won the FA Cup 11 times.