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 defender Joleon Lescott, who despite his starring role in last season's title success, has lost his place to youngster Matija Nastasic.
But Mancini has no intention of letting the 30-year-old England international go.
He said: "I can understand that Joleon wants to play because he is an England player and for him, if he doesn't play, it is difficult.
"But Joleon is a serious guy, working well always, even now if he doesn't play.
"We can't sell Joleon because we don't have other players."
The most concerning absence in the coming weeks will be that of midfield talisman Yaya Toure, who along with brother Kolo and striker Abdul Razak will join up with Ivory Coast for international duty this week.
City had hoped the trio could leave after Saturday's FA Cup third-round tie against Watford but now it seems the New Year's Day Stoke clash will be their last appearance.
Mancini said: "I don't understand why we lose three players for the African Cup. We are the only team that loses three players.
"We don't have a chance they can play against Watford. They have a (team) meeting on January 5, 12 o'clock. This is incredible.
"I spoke with their manager. He says they can't leave these players for this game, for three hours."
Mancini was involved in controversy on Boxing Day when he criticised the performance of referee Kevin Friend at Sunderland by saying he "ate too much for Christmas".
The Football Association has written to Mancini for an explanation but the Italian, who will stress he was joking, has not yet responded.
He said: "I thought they (FA) were on holiday for Christmas.
"I didn't receive a letter. The post is too slow in this moment.
"But I joked. It was a joke when I said the referee had a big lunch for Christmas."
When asked if he might escape punishment, Mancini said: "They can do what they want."