The former striker also believes a Champions League exit could actually be a good thing for the side.
The Gunners were once again in fine form on Saturday as they comfortably saw off a dangerous Watford side three nil at Vicarage Road.
The result left them sitting second in the table, just two points behind leaders Manchester City, but Shearer says they cannot get excited until they put in these kind of performances over ten months instead of just seven, as they have done in the past under Wenger.
“We’ve seen time and time again that Arsenal are brilliant at this time of the season then after Christmas see their form tail off,” he told Match of the Day.
“That’s what we need from Arsenal; they need to be brilliant for ten months of the season instead of seven months. Until they do that then there will always be doubts.”
The former striker has also suggested that exiting the Champions League could actually be a positive thing for Arsene Wenger’s side.
They have had a disastrously poor start to their European campaign this season, losing to both Dinamo Zagreb and Olympiacos, meaning they will have to get a positive result in their next two games against Bayern Munich.
But Shearer says it could be a good thing as it may help them to focus in the Premier League and more importantly, on pushing hard for a title challenge this season.
“I think going out of Europe will help them. If they go out, it will help them to try and progress in the Premier League,” he added.