The Gunners have not won any silverware since picking up the FA Cup in 2005, a barren run that has seen manager Arsene Wenger come under increasing criticism.
"It is no secret we need to win a trophy. How long has it been now, seven or eight years?" Wilshere told ESPN.
"The players feel the pressure and we have gotten close a few times like with the Carling Cup a couple of years ago. I think once we win one, others will follow."