The reigning Premier League champions are seemingly out of the race for this seasons title as they sit 15 points behind neighbours Manchester United but are in the final of the FA Cup where they will meet Wigan Athletic at Wembley on May 11.
Barry is aware that the league title is gone but says City must triumph in the cup final so they can at least bring something back to the Etihad Stadium this campaign.
"We knew this [the FA Cup] was the realistic chance of a trophy this year," Barry told reporters.
"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."