City moved within a game of claiming a third major piece of silverware in three years after holding off Chelsea 2-1 at Wembley to book a date with Wigan in next month's FA Cup final.
That would earn the club considerable consolation after a disappointing title defence in the Barclays Premier League and a failure to make an impression in Europe.
The situation represents a remarkable transformation for an outfit that had gone 35 years without success prior to winning the FA Cup in 2011.
Barry 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."