Referee Chris Foy awarded a free kick at the time and did not even book Aguero, but has been deemed to have already dealt with the incident sufficiently by the FA.
The Argentine was apparently riled at receiving an elbow to the ribs from Luiz moments earlier, and lunged in two-footed as the Brazilian lay prone on the floor following a tussle for possession.
After the match Luiz called on his opponent to apologize, saying: "Aguero's a great player, he needs to be honest with himself and say, 'I don't like to do bad tackles'. It was five seconds of anger and I forgive him."
Aguero had earlier doubled Manchester City's lead after Samir Nasri's first half opener, but Demba Ba set up a grandstand finish by pulling one back after the break.
City held on, however, and will face Wigan in the FA Cup final after the Latics overcame Millwall on Saturday.