Barry helped City into the FA Cup final in yesterday's semifinal win over Chelsea.
He said: "We knew this was the realistic chance of a trophy this year.
"Where the club is now, you don't really want seasons going past without winning a trophy.
"The FA Cup is a massive one. If we can win that, fantastic.
"Wembley is a fantastic place to come and play. The big players, as we have seen over the last few years, when we come to semi-finals and finals, they generally turn up and do the business.
"Hopefully they can continue that until the final."