The England midfielder left Villa in a £12million deal after spending 12 years at the club.
Barry told Sky Sports News: “People made out that I was apologising for it. I don’t feel the need to apologise for leaving Aston Villa.
Relationship
“I just wanted to state my reasons for leaving. I had been there for 12 years and had built a good relationship with the fans.
“Obviously it went a bit sour at the end of last summer for the way that saga ended.”
He added: “The club (Villa) have put the price on me and City have come in and paid the money really early in the transfer market.
“Once I talked to the manager, and the ambition about where they think they can head, and I spent a bit of time thinking about it and talking to a few friends and family, I made my decision and I’m very confident I’ve made the right move.
“Certainly from last summer, it was a tough summer for me, it dragged on and on.
“When a club are willing to pay the money early on and are willing to get a deal done – I felt very wanted.”
He added: “We have already seen the type of player Manchester City have been able to attract with the likes of Robinho and the type of players that they are being linked with.
“I think that this club has got everything in place to go and achieve big things and challenge right at the top.
“I am really looking forward to being a part of that and turning Manchester City into a team challenging for big honours. That would be a big thing for me.”
