Arsene Wenger's side have not lifted silverware since winning the 2005 FA Cup, and that competition appears their last genuine chance to secure a trophy this term.
The Gunners were dumped out of the Capital One Cup by Bradford, lie a distant sixth in Barclays Premier League, and face a daunting Champions League last-16 clash with Bayern Munich next month.
They must come through a third-round replay with Swansea to book an FA Cup fourth-round trip to Brighton, after being held to a 2-2 draw in south Wales on Sunday, but Wilshere and his team-mates are desperate to finally taste success.
"We all want a trophy," said the 21-year-old. "As players, when you finish your careers you look back and see how many trophies you have won, so we all want trophies, and the fans want trophies as well.
"We are hungry for trophies and if we get a trophy this year, then maybe it can open the way for a few more.
"We have got a good group of young players here and experienced players as well.
"So, if we get a trophy this year or in the next couple of years, we can really build something over the next few years.
"Obviously it is easy to sit here and say that when we get one trophy it will happen, but we need to get that first trophy. We know how tough the FA Cup is this year and we are still in the Champions League as well.
"So we are in a good position, we just need to make sure we get the results now."