City beat Chelsea in St Louis and New York during the short trip.
Barry said: "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.
"You have to learn and we have to come back fighting strong for next season.
"The lads are already looking forward to it.
"The club needs to keep winning trophies. We've had a disappointing season in not picking one up but if we can keep setting high standards the club will move forward and, as a team, we will move forward."