Walcott, who has recently committed his long-term future to the north London club, confesses he can understand the supporters' impatience.
He said: "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.
"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."