City ran out 1-0 winners in north London and will face Stoke in the final in May but the United pair felt that the controversial youngster had acted irresponsibly when the final whistle went by holding his badge in front of the Red Devils' fans.
The actions of the 20-year-old led to Ferdinand shouting him down as players and coaches from both sides squared up on the Wembley turf.
Tweeting after the game, Ferdinand moved to justify the actions that may land him in trouble with the FA after referee Mike Dean noted the incident in his report
He said: “If you score a goal and give a bit to opposing fans I kind of accept that, but at the final whistle go to your own fans and enjoy it, not opposing fans.”
Portuguese winger Nani also questioned the actions of the hot-headed former Inter man, who delivered one of his best performances yet for City since moving from the European champions in the summer.
Nani added: “Rio was upset because he [Balotelli] was not fair, it was disrespectful and our players were unhappy about that.”
However, City coach David Platt, who looked to calm Ferdinand down during the melee, has insisted that the incident should not distract attention from what was a glorious day for Roberto Mancini's side.
He said: “His [Balotelli’s] performance on the pitch showed a great deal more maturity, the scenes at the final whistle should not have happened but let’s not let that mar what was a great day for us. He is young and can’t stay out of the headlines and a lot is said about that.
“Perhaps he shouldn’t have done what he did in terms of going over to the Man United fans and it isn’t a case of defending him, it was something and nothing at the final whistle.”