The Gunners were denied a place in the FA Cup fourth round by Danny Graham’s late equaliser for Swansea on Sunday, setting up a replay at The Emirates next week.
“We all want a trophy,” said Wilshere. “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.”