Walcott says they must all build on a superb end to the previous campaign which saw the Gunners go on a 10-match unbeaten league run to snatch fourth place ahead of Tottenham and with it secure another shot at the Champions League, with a two-legged play-off ahead next month.
"The way we ended the season last year, 11 games undefeated - we need to do it from the start, which I believe we can," Walcott told arsenal.com.
"The manager shows so much belief in us in every single game so we need to step up and I think we have got a very good chance of challenging this season.
"Every game in the Premier League is very tough and very interesting.
"It always comes down to the last few games, so we need to believe in ourselves."