The Gunners have not won a trophy since their triumph in the competition in 2005.
Oxlade-Chamberlain is hoping that a new era of success can begin at Arsenal, starting with the FA Cup trophy.
"Once you do get that experience of winning the first one, you automatically build confidence," he told reporters. "You can go and do it again.
"I always hear commentators talking about squads that have been around and won things. They always mention the experience of winning, knowing what it takes, and they've only got that through winning trophies.
"We are in a position where we can make it happen, in a position where it is our responsibility to take that opportunity."
Arsenal face Wigan Athletic tomorrow for a place in the FA Cup final.