Arsene Wenger has won three league titles and four FA Cups during his time at the Gunners helm, although there has been nothing added to that trophy collection since 2005.
It is a stick often used to beat the north Londoners with, but maybe not for much longer.
Despite missing a host of first-team players through injury, Arsenal opened up their Champions League campaign with a 2-1 win at Marseille on Wednesday.
That was a club record 10th successive win on the road, highlighting why Walcott believes that barren run may soon be coming to an end.
"I think we'll push on and we can definitely challenge this year, for sure," he said.
"There is so much belief in this team at the moment and I think it's showing. We just need to make sure we get that home form going now, the away form is absolutely fantastic.
"It's 10 successive wins away from home, someone told me in the dressing room. It's a record. I didn't know that until after the game.
"To be part of a team that has done that, in the amount of years that Arsenal have existed, is a great honour and a great achievement for everyone.
"It just shows how good and how talented these players are.
"We haven't got the biggest squad in the world and we've got a lot of injuries, which doesn't help, but the players that are playing and contributing and the players that aren't playing as well, it's important that everyone is focused.
"We've got to stay fit, which is crucial as well - we don't want to lose any more players.
"As soon as the players come back there is going to be more competition for places as well. That's only going to be a good thing for Arsenal."
Arsenal's threadbare squad will be stretched over the coming weeks, with league matches against Stoke, West Brom and Swansea before the month is out.
There is no let-up in October, with vital Group F clash with Napoli and Borussia Dortmund at the Emirates Stadium.
Jack Wilshere believes they can go onto win the group following victory in Marseille, but Walcott is urging caution.
"We don't want to look too far ahead," said the forward, who opened the scoring at the Stade Velodrome.
"We've got to concentrate on Sunday against Stoke first of all.
"It's a great start to the competition. We've got players who are playing fantastically well.
"We always felt we didn't want to lose, so to get the three points was an absolute bonus."