The Brazil international was the victim of a two-footed lunge by the Argentina striker, who had earlier scored the vital second goal to send the 2011 FA Cup winners into the final
The Argentina striker scored City's crucial second goal in the match at Wembley but later lunged in at Brazil international Luiz in the 82nd minute.
And Luiz, who also appeared to try and elbow Aguero, believes the match-winner should say sorry for his challenge.
Luiz told reporters: "Many people say to me about this tackle. I didn't see it because it was in the back of me. I cannot speak about that.
"I felt it a little bit. Aguero is a great player and I think he needs to be honest with himself and say: 'I don't like to do bad tackles, I don't like to do that.'
"I forgive everyone in my life. People are happy when Aguero is scoring goals, doing things in the game. Many people have said to me: 'Sorry this is not me and not good for the football.' Many kids see the game, watch the game and want to see good things and not bad things."
And when asked whether he would apologize were he in the Argentine's shoes, Luiz was adamant that he would.
He added: "Of course, I would apologize to everyone. I want just to show people good things – football is beautiful when you play games like that. Both teams tried to win, both created opportunities and tried good things.
"Sometimes in the games people have five seconds, be angry and do things you don't like to do. I think that. I never saw Aguero do bad tackles on other players. I think it was five-second angry and I forgive him."