"The Champions League is obviously a major target and I want to help the club to that level," said the England midfielder.
"I believe Manchester City can be playing Champions League football while I am here, otherwise I wouldn't have joined, but it won't happen overnight and there is a lot of hard work to be done first.
"I fully understand why people raised their eyebrows about this move but I'm looking to the future and I'm confident that City are heading in the direction that I want to go.
"I'm certain that we can be challenging for major honours and I aim to play my part. I've been around long enough for people to know what to expect from me and I'm confident my performances will keep our fans happy."
Barry's powerful, industrious drive at the centre of City's midfield will be a key factor in manager Mark Hughes' strategy for meeting his top-six target and maybe hammering on the door of the so-called big four.
He said: "I learned a lot last season at Villa about just how hard it is to try and get a grip on that top-four place. It's a lot of hard work and you have to stick together as a team.
"I said that if Villa had finished in the top four I would have stayed - and I would have kept my word. It was something we tried to achieve and it would have been wrong of me to leave had we done it."