Wilshere made his return to first-team action as a substitute in Monday's 3-1 win at Hull after five months out following an ankle operation, and said the Gunners were determined to secure the runners-up spot behind Chelsea.
The England midfielder told Arsenal's official website: "(Finishing second) would set a marker for next season and would be a progression from last year.
"The last few seasons we've finished fourth so to finish two places ahead of that would be a massive progression for us and hopefully will give us confidence going into next season."
Manager Arsene Wenger said Wilshere's 20 minutes on the pitch showed he had recovered all his "burst and acceleration" and the 23-year-old's display should guarantee at least a seat on the bench for the FA Cup final against Aston Villa.
For Wilshere, merely returning to action was good enough.
He added: "That's the most important thing for me
It's frustrating when you're out but when you're back on the pitch it makes up for all the time you spent injured.
"It's much better for me to come into a team who are winning and playing as well as that
It's easy because you can fit in when the boss is ready to include you.
"I'm just happy to get back on the pitch and get some minutes under my belt
I feel fitter for it, I'll train next week and hopefully get some minutes next week as well."
Wenger suggested Wilshere might even have been trying too hard to make an impact after coming on for Aaron Ramsey.
"It's great and he's sharp," said Wenger
"Maybe he felt too sharp because he wanted to always make the difference but it's good.
"You could see that he has found his burst again
Let's be patient with him, not too demanding either
It is interesting that he's back."
Arsenal skipper Per Mertesacker said the Gunners will need to be more consistent next season, especially at the start of the campaign.
He told the Evening Standard: "The points we dropped at the start which was 10 or 11 points, it was a gap we could not close.
"We were consistent, especially in 2015, but not consistent enough or Chelsea didn't win enough points and we couldn't win against them.
"I would say when we look just at ourselves, that's what we feel."
Source : PA