The Gunners have not won any silverware since the 2005 FA Cup and were beaten in the 2011 League Cup final by Birmingham City.
Wilshere has said that the North London outfit need to look to rectify their lack of trophies next season.
"We nearly won a trophy two years ago [losing the League Cup Final] and it's so important to win something. We really need to be up there challenging," Wilshere told The Mirror.
"We need to win the big games. Last year, I think we only won once against the other big teams. We need to improve on that. It's such an important year for us. I feel we can win trophies this season. It's a big year for me and for the team.
"Everything has changed. Ferguson has gone [as Manchester United manager]. Chelsea and City have changed their managers. We have to set our targets high.
Wilshere could make his return for the Gunners when they play Vietnam in a pre-season friendly today.