The Gunners finished last season on a 10-game unbeaten run, which propelled them into the top four, securing Champions League qualification.
Walcott told Sky Sports News: "It is quite frustrating at times, because we should have done that at the start of the season. Who knows where we would have been.
"We need to remember those moments that we had and make sure we do it from the start, because we could be challenging for anything. We could beat anyone.
"We want that sort of fear factor, especially at the Emirates."
Walcott scored 21 goals in 44 appearances for the Gunners last season.