The Gunners ended the campaign in strong form, recovering from defeat at Tottenham in March to beat Bayern Munich away and then win eight from the last 10 league games as they battled back to clinch fourth spot ahead of their north-London rivals - and with it another shot at Champions League football.
By contrast, Arsenal had secured only four victories from the opening 10 matches - which included defeats at Chelsea, Norwich and Manchester United. Indeed, Arsene Wenger's side dropped as low as 10th place when they were beaten at home by Swansea on December 1.
Wilshere, 21, knows it is a scenario which cannot be repeated if Arsenal are serious about lasting the distance in 2013/14.
"The games earlier on don't decide our season but we have got to think that we have to win them, because that is what champions do," Wilshere, who is set for ankle surgery which will rule him out of England's friendlies against Republic of Ireland and Brazil, said in an interview with Arsenal Player.
"The likes of Manchester United go away and win games and leave you thinking, 'they keep winning and winning' and at the end of the season the points tally shows that.
"That is what we have to do [to challenge for the title]."