The England international believes the Gunners must maintain the confidence they found to exceed expectations after a poor start, and recalled the nerves of their final day win
The Gunners secured Champions League football for a 15th consecutive season with a final day win over West Brom but failed to mount a serious challenge for honours this term.
And the 23-year-old forward has set his sights on ending that barren run next season, injuries allowing.
"We have to push on, as it’s been so long without a trophy now." Walcott told the Evening Standard.
"We need to start believing a bit more. The belief came in September. If we can do that right from the start and keep people fit, you never know where it will take us next year."
The north London side suffered a shaky start to the season, dropping as low as 17th after suffering an 8-2 defeat to Manchester United and an embarrassing loss to Blackburn Rovers.
However, they have since undergone a remarkable transformation to charge up the table and claimed third ahead of north London rivals Tottenham on a nervy last day.
The winger acknowledged the turnaround, adding: "Third is fantastic, you wouldn’t have thought we would achieve that, the way we started the season.
He added: "When I was on the bench I could see that Tottenham scored very early - even the boss was asking what the results were!"