Barry has signed with Everton on a season-long loan.
He revealed: "Virtually straight away at the end of the season and at the start of pre-season it was made clear that I wasn't going to be guaranteed regular first-team football (at City).
"Being 32 in a big squad with a lot of players, I could have dealt with that.
"But as pre-season went on and then the first games came, it was pretty clear that I wasn't going to feature in squads and that I was going to have to wait for a couple of injuries.
"So that's when I started thinking it could be time to start looking elsewhere for regular football."
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