The England international admitted the now-managerless club's frustration as 2012-13 draws to a close but, with a fresh start under a new boss looming, anticipates better times ahead.
"We're disappointed with the overall finishing position in the league and to lose the FA Cup final but you can't win them all," Barry told reporters.
"You have to learn and we have to come back fighting strong for next season. The lads are already looking forward to it.
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Manuel Pellegrini is expected to take over at the Etihad Stadium following the dismissal of Roberto Mancini and Barry is looking forward to the new beginning regardless of the identity of the Italian's replacement.
"For every player it is going to be a fresh start," Barry added. "It is down to us to work hard.
"The players don't know too much about who is coming in but I am sure whoever does come in is going to do a fantastic job.
"There is a lot of talk about Pellegrini at the moment. Personally I don't know too much but people who do know him and have played with him speak highly of him."