Arsenal rallied over the run-in last season to secure fourth place ahead of Tottenham following a 10-match unbeaten league run.
Manager Arsene Wenger believes his players can draw from that experience to hit the ground running when the new campaign kicks off against Aston Villa this weekend to mount a long-overdue sustained assault on the championship.
England midfielder Wilshere insists the players will pay little attention to those who say they do not have what it takes to go the distance with Manchester United, Chelsea and Manchester City.
In an interview with Sport magazine, Wilshere said: "I have been reading things like: 'Arsenal aren't title contenders', but we have had that for years.
"We feel we have a great squad, as we showed towards the end of last season, when we went 11 games unbeaten [after losing that game at Tottenham].
"So if we can reproduce that form, then we have a chance.
"When we had to get the results, we went out there and got them, and that's what we need to take into this season."
Arsenal last lifted silverware with the FA Cup in 2005 and Wilshere accepts the barren run has been allowed to go on for too long.
"We understand the fans' frustration, because we care as well," he added.
"Arsenal used to be a team that won everything, you know - trophies and titles, but now we haven't won anything for eight years, so we know what we have to do.
"It is time to start producing trophies and being closer to the top of the league at the end of the season.
"We don't just want to be fighting for fourth place - we want to be up there with the likes of Chelsea, Manchester City and Manchester United. We feel we are good enough to be there.
"Last season, we lost games in cup competitions in which we could have been there at the end.
"We lost against Bradford away [in the Capital One Cup] and Blackburn at home [in the FA Cup].
"We should never be losing games like that, but this year we have to get over that, grow up a bit and realise that we need a trophy - Arsenal's too good not to be winning trophies.
"We will be in four competitions this year. We know we have to win one of them."