Man City's Sergio Aguero escaped without punishment from referee Chris Foy after the Argentine striker threw himself into a ferocious two-footed lunge on Luiz late in the second half at Wembley on Sunday.
Luiz was lying prone on the turf after tangling with Aguero moments earlier and the centre-back appeared to take the full force of the challenge.
Somehow Foy and his assistants missed the foul but fortunately Luiz was able to finish the match, although City's 2-1 win added insult to the injury which left him with stud marks on his body.
Luiz was keen to point out that he didn't think Aguero was a malicious player who had meant to harm the centre-back.
However, he believes Aguero should apologise to set a good example to fans across the world.
"I forgive everybody in my life but Aguero is a great player and he needs to honest with himself and say I don't like to do bad tackles," Luiz said.
"If it was the opposite and I did the tackle, I would say 'sorry this is not me, this is not good for football'. Kids watch the game and need to see good things.
"We need to show football is beautiful. In games like this both teams want to win. Sometimes people can be angry and do things they don't want to do.
"I think it was that because I never saw Aguero doing bad tackles on other players.
"I didn't speak to him after the game. I have a good heart. I don't like to beat on people and talk in a bad way. I just like to play football."
Aguero's tackle, and the controversy over Foy's failure to award Chelsea a late penalty for Vincent Kompany's tug on Fernando Torres, left Luiz and his team-mates with a bitter taste as they headed home from Wembley.
But the Brazilian conceded Chelsea had only themselves to blame for a slow start that left them two goals down by the 66th minute.
"They were better in the first half," Luiz said. "After half-time we woke up and created a lot of opportunities. We just couldn't get the result.
"We didn't want to start slow. We couldn't score when we didn't have the ball and we spoke about that at half-time."
Sunday's defeat leaves Chelsea with the Europa League as their only remaining chance of silverware -- they face Basel in the first leg of the semi-finals later this month.
Luiz believes winning that competition and qualifying for the Champions League via a top-four finish in the Premier League would still constitute a successful season.
"We can still stay in the top four positions and win another European title, so we work for that," he said.
"If you win the Europa League and qualify for the Champions League of course the season is a success.
"Some big teams in Europe won't win titles this year for sure."
Rafael Benitez's side are back in action at Fulham on Wednesday and with a busy schedule until the end of the season, the Spaniard has to decide how often he is willing to play John Terry and Frank Lampard.
The two aging Chelsea stars had played in virtually every one of their club's major Cup occasions over the last decade.
But both were unused substitutes on Sunday, prompting Benitez to defend his selection.
"What I'm trying to say is that to play two games a week is not easy for some players in some positions, not just John," Benitez said.
"Sometimes you see the players are tired, so you have to rotate, but we had the intensity we needed, so I think we're OK.
"Now we have to concentrate on the league. Fulham will be a massive game. We'll try to keep the players thinking positive."