The Gunners are seven points adrift of fourth-place Spurs (with a game in hand) after their 2-1 defeat to Chelsea at the weekend.
And Walcott thinks the Arsenal squad are talented enough to challenge their rivals, but they need to show more confidence.
He's quoted in The Daily Mirror as saying: "I think there's a lack of belief as to how good we can be. We've got some very, very good players here. I think players don't believe they are good enough at times. But, trust me, I see them every day in training and they should believe that.
"We need to start realising how good we are. We showed some great stuff in the second half at Chelsea but it's time we did that from the start on.
"If we just look at the second half, forget the first half, I think we were too slow, sloppy closing down and we've got to show more commitment. We gave them too much space as well.
"As soon as we pressurised them a bit more, pushed up higher and the manager said if we got that early goal then it would be different.
"It wasn't meant to be, but we gave the manager something to think about and we can't be slow off the blocks like that again.
"We've got a great bunch here, a great manager and he always puts it upon himself which is hard because we are the players out there every week. We try to win for him, we need to win for him because he's been very helpful for us young players coming through."
Walcott also insisted that Arsenal must concentrate on their own game, rather than Tottenham's.
"Last year, we were so many points behind no-one ever thought we would make it. We've got a game in hand but we need to clock up these points fast.
"The gap doesn't worry us. We can't worry about them (Spurs).
"We hope they do drop points, but we've got to concentrate on ourselves, win games - and we've got a big game on Wednesday when we have to pick ourselves up
"We are ready, it's our game in hand, we have to get three points and, no disrespect to West Ham, we should win that game.
"This team is getting better every year. We don't want to be standing still. We need to be right up there at the end of the season, Champions League football and competing as well.
"It means a lot. It's one of the reasons why I decided to stay. I feel we can and should be there. I still think we will (make the top four) and I think we'll be fine.
"The Champions League is massive. I've had so much experience. I'm only 23 and yet I've played so much in the Champions League and not many players my age would have had that experience.
"I know how good it is, I know that the players in our dressing room will get better from playing in the Champions League, playing against the best in the world.
"It turns you into a better player, definitely. You go to different stadiums, you experience that. We went to Schalke recently and I'd already been there from the World Cup 2006 and it's good to go to these places, be prepared. You can't get bigger than the Champions League."