The prolific Dutchman was heavily linked with the Barclays Premier League champions before opting to sign for rivals Manchester United in a reported £22million 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."
Van Persie, who scored 37 goals for Arsenal last season, sparked a scramble for his services when he revealed he would not be renewing his contract at the Emirates Stadium.
When he was unveiled as a United player in August he said he had listened to the "little boy" inside him when making his choice of club.
Mancini said he knew why City failed in their bid but would not give a reason.
When asked if it related to money, Mancini said: "It is not the problem."
Van Persie has hit the ground running at Old Trafford and has already scored 17 times for United in all competitions.
With United beginning 2013 with a seven-point lead at the top of the Premier League, Mancini believes Van Persie is the key difference between the two sides from last season.
He said: "I think Van Persie, for United, is an important player.
"It is clear he changed this situation. In this moment, the difference is this."
Mancini has often bemoaned the output of his own strikers in recent weeks.
Sergio Aguero, Carlos Tevez, Edin Dzeko and Mario Balotelli have all struggled for goals of late - a problem highlighted in the shock Boxing Day loss at Sunderland.
Dzeko responded by scoring twice at Norwich on Saturday and Aguero was also on target in a 4-3 win.
Mancini insists he retains faith in his attacking options even though he did not get the player he wanted last summer.
He said: "I am happy, very happy. Last year we were the team that scored the most goals in the Premier League.
"But when you can improve your team with another top player, this is important.
"With Van Persie we would play with three strikers sometimes."
While Mancini has admitted injuries and African Nations Cup absences may force him into the transfer market in January, he is adamant he will not be selling players.
It had widely been assumed City would need to move players on to bring in new faces.
One player linked with a possible exit is Balotelli, who has performed well below his best this season.
But Mancini feels City's owners do not want to see the Italian leave.
"Sheikh Mansour likes Balotelli because he recognises the talent and he exports the name of City over the world," Mancini said in The Sun.
"We need to realise Mario was signed as a major investment and this is not a club that throws its capital through the window.
"I think Mario will stay but the future depends mostly on him."