The midfielder has played more than 400 Premier League games and has been in the England set-up for over 10 years now.
In 12 years as a professional, the 29-year-old has one runners'-up medal from the FA Cup final in 2000 and an Intertoto Cup triumph from 2001 - both with Aston Villa.
However, Barry is conscious that time is ticking and is eager to finally win something, telling The Independent: "I have played a lot of games, had a good international career and picked up a lot of caps but it is not going to be complete without winning trophies so that is my main goal."
Roberto Mancini's side were knocked out of the Carling Cup by West Brom at The Hawthorns in midweek, but Barry feels the squad will be even more determined to succeed.
"I was sitting at home watching the Carling Cup game thinking 'That's another trophy gone'. It is hard to take when you go out of these competitions but it just makes you more determined to succeed eventually," he explained.
"At a club like this people are just waiting for it to happen but there is so much hard work that needs to go in. Having been around I know how difficult it is to get results in this league.
"It doesn't just happen by buying players. It needs a lot of hard work.
"That is why the first trophy can be the most important one and if we can get one the sooner the better.
"The first trophy here is going to be the most important.
"The fans have a rivalry with Manchester United and you look at how successful they have been, it is a case of getting over that line, winning a trophy and stopping the banter. The quicker the better."