The Emirates Stadium club have gone eight years without a piece of silverware and that has added pressure on boss Arsene Wenger.
But a 10-game unbeaten run at the end of last season helped secure another finish inside the Premier League's top four and Walcott hopes to continue that momentum.
"It is quite frustrating at times, because we should have done that at the start of the season," he told Sky Sports. "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."