Luiz admitted he was "angry" with Aguero after his lunge towards the end of City's dramatic 2-1 victory and accused him of setting a bad example.
He said: "Aguero is a great player but he needs to be honest with himself and say, 'I don't like to do bad tackles'.
"Kids see the game and they want to see the good things and not the bad - I would apologise. Football is beautiful, but sometimes in games people have five seconds like that - I forgive him because I have a good heart. I don't like to beat people."