bringing United victory after Pablo Zabaleta looked to have claimed a share of the spoils with a late equaliser.
Van Persie's free-kick took a telling deflection off Nasri, who appeared to shy away as the ball arrowed towards him, while Balotelli stormed straight down the tunnel after being substituted in the 52nd minute.
Carlos Tevez, Balotelli's replacement, stepped out of the defensive wall as van Persie prepared to strike his decisive set-piece, but Mancini dismissed suggestions he had instructed the Argentine to move.
"It was a dangerous free-kick," said the Italian. "I don't know why (Tevez left the wall), but we made a mistake there."
Tevez's departure from the wall left City with only three players to face van Persie's shot, but Mancini said Nasri's behaviour was more baffling.
"In the last free-kick, we put only three players there," he said.
"Were there three? We had two and a half. We didn't cover very well."
He added: "We dominated the second half, but we can't concede a goal like this. If it hits you in the face, it hits you in the face.
"In the history of football, there are teams who didn't win championships for this reason. I'm really upset we didn't win this game."
Mancini was also less than impressed with the display of Balotelli, who came back into the starting XI after starting City's previous two games on the bench, only to leave the fray before the hour with little to show for his efforts.
"I love Mario like a guy, and as a player, but I think it's important for him to start to think about his job if he wants to play well," said Mancini, who dropped his countryman from the City squad earlier in the season over his lack of application in training.
"When you have a player with Mario's quality, you can't believe that he throws his quality out of the window.
"I've seen players in my life with fantastic quality who ended up with nothing and I don't want Mario to finish like these players, because it will be bad for him."
To make matters worse for City, who were eliminated from all European competition in mid-week, they lost captain Vincent Kompany to an apparent groin injury midway through the first half.
Mancini was also critical of referee Martin Atkinson and his officiating team, claiming they "made some mistakes", but he pledged not to throw in the towel despite City now trailing United by six points in the Premier League.
"We need four or five wins in a row, but we have a good spirit for this," he said.