Aaron Ramsey scored an extra-time winner at Wembley on Saturday to defeat Hull City 3-2, having gone two down inside eight minutes, and seal Arsenal's first trophy in nine years.
And Wilshere feels it was just reward for the supporters who have stuck by the team through their infamous barren run.
"It's hard to put into words (what this victory means to me)," he told Sky Sports News. "It's been nine years now - we've waited a long time for this.
"We've worked hard and the manager has worked hard but most of all this is for the fans who fill the stadium every week. This one is for them.
"It was a bad start (in the final). We've done that a few times this season and been punished but we knew if we got a goal before half-time we could go on and win it.
"We're a fit team and we've got quality as well. That's a good mixture and we showed that.
"We had a hard run (in the competition) as well so you can't say that we didn't deserve it. We showed the character that we've shown all season in the final and fair play to the boys.
"Now that we have got the first hurdle out of the way hopefully it will give us a boost for the seasons to come.
"We've shown character for the last couple of years but (Saturday) was a testament to the players.
"We overcame a big hurdle and we're very proud of that. We're very proud of how far we came in the competition and we did it for all these people."
