The prolific Dutchman was heavily linked with the Premier League champions before opting to sign for rivals Manchester United in a reported £22 million deal.
Mancini has previously admitted he was interested in signing the 29-year-old but has only now indicated how strongly City pursued him.
The Italian said: "We wanted Van Persie because we knew he could be an important player.
"He is totally different from our other strikers. We wanted him for the Champions League and for the Premier League.
"We were very close. We were sure he was for us but this did not happen and now we can do nothing.
"We were very close three or four months before he joined United."