Arsene Wenger’s men reclaimed top spot with Sunday’s 0-0 draw at Stoke, but they are only above second-placed surprise package Leicester on goal difference, while Manchester City are just a point worse off in third.
Tottenham and Manchester United, fourth and fifth respectively, also look to be still in the mix.
And Walcott said: “You can’t tell what’s going to happen, it’s just so tight.
“With the amount of teams that could potentially win this league, it’s probably going to be the most exciting Premier League for a neutral ever, I think.
“No one can call it but we’re top and we can be proud of that at this moment in time.”
Arsenal went into Sunday’s contest having lost on their previous two visits to the Britannia Stadium and won only once in their last eight trips there.
Key to the result they secured this time was their goalkeeper Petr Cech, who made several excellent saves to mark the latest in a string of fine performances he has produced since joining from Chelsea last summer.
Arsenal, last crowned Premier League champions in 2004, have in Cech acquired a player who has won the title four times since then, including last season.
Walcott, with the club since 2006, believes there is greater mental toughness in the camp now than he has ever known before.
He is in no doubt Cech has been a vital part of that and is someone he and his team-mates must continue to take inspiration from.
“The mental strength in this dressing room’s the strongest it’s ever been,” Walcott said.
“When you have the likes of Petr Cech coming in, he just enhances that. He’s a leader.
“We’ve just got to look at him because he’s obviously been at the top level and won many things. If we all have the belief he’s got, we can push on.”
After Sunday’s game – in which Cech’s Stoke counterpart Jack Butland was also a stand-out performer – Gunners boss Wenger praised his players for the “physical response” and “fighting spirit” they had shown in what he had regarded as a “battle”.
And those words were echoed by Walcott.
“We felt from the start physically we were up for the fight and the battle,” the 26-year-old England international said.
“It’s an improvement from previous performances here. We’ve got to be proud of that point.”
There were no bookings in the game and Stoke boss Mark Hughes, who has tried to implement a more aesthetically-pleasing brand of football at the club since taking charge in 2013, took issue with Wenger suggesting the hosts had made it a physical contest.
Potters midfielder Ibrahim Afellay thinks Hughes is overseeing a good combination of styles.
“We have creative players and also the guys that were already here, they are doing very well,” he said.
“You see the hand of the coach – he makes a big difference.
“He has changed Stoke’s play and you can see – to work very hard is the most important thing, and then you also play football. This is the best combination, I think.”
Stoke are seventh, six points off the top four.