Walcott says the character of the team should not be questioned, but admits their mixed performances have held them back for too long.
"If we get a bad result, you see a reaction," he told Arsenal Player. "We shouldn't have to get a bad result and then perform well in the next game. It should always be there.
"The guys have got it. Mentally, they are very strong. It's realising how we cope when we come back from those disappointing results. We just need to do it every week - it's as simple as that.
"There's great potential there. We've had too much experience now to be challenging for fourth. We need to be challenging for the Premier League because that's what we want to be known for.
"We want to be in the history books we need to win something now."