Villa could only manage a sixth-place finish last season despite being fourth in mid-March.
Martin O'Neill's side faded in the run-in after a promising spell that saw them on the brink of securing a place in Europe's elite competition.
Barry, 28, who left Villa to join Premier League rivals City in a £12million deal this summer admits his future very much depended on the Midlands club's achievements last season.
Had they secured qualification to the Champions League, he admits he would have been more inclined to stay.
Aspirations"If Villa had finished fourth I would have stayed," he said. "I would have enjoyed playing Champions League football at Villa Park.
"It would have been wrong for me to have left had this been achieved.
"But once it was looking like Villa weren't going to make it then my future became unclear.
"The whole point of me coming here was to have a change, something that excites me.
"Playing in the Champions League with Manchester City is viable. The manager has convinced me we can reach these heights."
ReassuranceBarry admits he sought reassurance from the club's billionaire owners that Mark Hughes would remain in charge before agreeing a deal.
"I have to look at the fact that I've joined a club that is not competing in European football," he added.
"People will question this decision but I'm confident that in a couple of years time people will realise I made the right decision.
"We all know about the ambition of this club and it excites me. They want to sign top international players and it just felt like the right thing to do to come here.
"The first question I wanted to know about was the future of the manager. I've seen it before. Players join clubs then two months later the manager is gone and their future is uncertain.
"That was the last thing I wanted to happen here."