The Gunners' last silverware came in the form of the 2005 FA Cup, and while they have appeared in several cup finals since then, they have failed to win any of them.
However, the England international believes that the North Londoners have a great chance to end their hoodoo this year in both the FA Cup and Champions League.
"It's been a long time [since we won anything], everyone knows that and as players we know it's not good enough. We need to be achieving what Arsenal did in previous history," said Walcott.
"I want to be part of that and I'm definitely ready for the battle. We've got a great chance in the FA Cup and, although we've got a very tough game against Bayern [in the Champions League], I believe we can win that as well.
"The next step will come once we win that first medal. Hopefully once we do that we can win more and that's my goal."
Arsenal travel to face Sunderland on Saturday.