The Gunners have not won a trophy for eight seasons but have a good chance to end that in this year's cup, in which they face Wigan in the semi-finals on Saturday.
England international Oxlade-Chamberlain, 20, insists that while the current squad are not burdened by the weight of expectation, they are all aware of the importance of breaking their barren run.
"It is just good to get into winning ways, to win a trophy, to be able to go the whole journey as a team and win it, that is a massive experience for a team like us, who are fairly new together," he said.
"It is definitely a springboard and a confidence boost going on to the future.
"Once you do get that experience of winning the first one, you automatically build confidence that you can go on and do that again and again and again. That experience is vital.
"I always hear commentators talking about squads that have been around and that have won things, they always mention the experience of winning, and knowing what it takes to win. They have only got that through winning trophies, and winning competitions.
"That is definitely something that will help this team to go on and push forward and be successful in the future, but it is just getting to that first one, and that is a lot easier said than done.
"We are all desperate to win, there is no doubt about that, but for me it is not so much that I am really impatient, I am more interested in trying to play as well as I can, and help the team whenever I am needed.
"I believe that with the team that we have here, it will come."
Despite Arsenal's status as favourites for the last-four clash against Championship side Wigan, Oxlade-Chamberlain says he and his team-mates will not be underestimating the Latics, who have already beaten Manchester City en route to the semis.
"We don't think we are massive favourites and they are underdogs. We know it will be really hard," he said.
"If they can beat Man City, on their day they can beat us, and it is our responsibility to make sure that does not happen by not taking anything for granted and approaching the game in the right manner.
"We know what is in store and what they are capable of, so we need to give them the respect they deserve and do what we need to do as a team."