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, and the 21-year-old said in an interview with Arsenal Player: "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."
Arsenal's recorded opening 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, who is set for ankle surgery, knows it is a scenario which cannot be repeated if Arsenal are serious about lasting the distance in 2013/14, and he added: "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)."
Wilshere feels Arsenal must step up their form in the head-to-head against their direct rivals, having lost both at home and away to Chelsea, been beaten at the Emirates Stadium by Manchester City and having drawn with United when they came to north London just after being crowned champions.
"We also have to improve our record against the big teams," the England man said. "It has not been great this season and if you want to become champions you have to beat those sides."
To help facilitate closing the gap on United, City and Chelsea, Arsenal are expected to significantly bolster their squad this summer as Wenger finally dips into his £100million war chest, set to be backed up by new lucrative marketing deals.
The club are also set to get Andrey Arshavin, Marouane Chamakh, Nicklas Bendtner, Denilson, Sebastien Squillaci and Korean forward Park Chu-young all off the wage bill. However, Gremio have suggested they are unlikely to take up a permanent deal for Andre Santos, who is currently on loan back in Brazil.