Mancini insists City's progress is already sending shockwaves around Europe. And he warned they are going to get better after the club applied for planning permission to build a £100m training ground that will include a youth academy to rival anything there is in the game.
Mancini said: "People are mistaken about Manchester City. They accuse us of spending more money than anyone this year and every time they said that they are mistaken.
"If you look, there are a minimum of five clubs who spent more than we did during the summer and this seems to be forgotten.
"Everyone says we have spent a lot of money but so what? To us it isn't important. We just want to progress, to become a better club, and I think some people respect that.
"In Italy and Spain we are now regarded as a top team. All the people in those countries now speak about City as being one of the top clubs in Europe.
"That is good. Many people now talk well about City."
He added: "If we want to be like the other top teams, we have to be winners.
"That can take time. This is our first time in the Champions League. But in football you never say never. Anything can happen. Last season, Schalke 04 arrived in the semi-final so I think we should have the belief that we can also do that.
"With the new training facility our club has planned, one day we will be much bigger and better.
"That will mean we can develop young players and that's important."