The Gunners endured a frustrating end to 2010/11, losing the League Cup final to Birmingham City before crashing out of the Champions League and FA Cup in the space of two weeks.
The Emirates Stadium outfit then slid down to fourth place in the Premier League, meaning they will now be forced to take part in the Champions League play-off round next month.
And Wilshere believes Wenger must add to the squad if the Gunners are to end their trophy drought.
"It would mean everything to win a trophy this season," Wilshere told Arsenal's official website. "Last season we just missed out. That last minute against Birmingham ruined everything in a way.
"We are always there or thereabouts at the end of the season. But we need to stay strong and maybe make a few more signings and we will be alright.
"We have been saying in the last few seasons that we need a bit more toughness but the boss knows what he is doing. Hopefully he will bring what we need in and we will win something at the end of the season."
Wilshere was afforded a longer than expected summer break after being withdrawn from the England squad for the European Under-21 Championships in Denmark, and the 19-year-old feels that extended break could stand him in good stead for the coming season.
"Before the tournament we spoke about how important it was to get my rest and now I feel really rested.
"I will be ready for the start of the season. I went away on a few holidays and put my feet up on a beach and relaxed. I feel refreshed now.
"Of course there was a part of me that wanted to be playing. When you are watching the games you want to play but you have to see the bigger picture.
"The bigger picture for me was to rest and be ready because we have got a Champions League qualifier and a hard start."
