Luiz's comments come after Chelsea head coach Jose Mourinho insisted that the Brazilian should have been sent off for elbowing Costa.
However, Luiz, who used to play for Chelsea before moving to the French club, made it clear that he never would elbow Costa since he is a good friend of his.
Luiz did go on to say that Costa had elbowed him during the match, which finished 2-2 and saw Paris St-Germain proceed to the quarter-finals on the away goals rule.
"Mourinho can say what he wants," Luiz was quoted as saying by The Sun. "Maybe he should talk about when Costa gave me an elbow in the diaphragm early on. I didn't elbow Costa. He's a very good friend and a fantastic guy.
"It's always a battle to play against him and I'm very happy for him."
Luiz was also seen exchanging words with Mourinho after Paris St-Germain striker Zlatan Ibrahimovic was sent off in the 31st minute for his challenge on Chelsea midfielder Oscar.
When asked what he had said to his former coach, Luiz said: "When I was by the touchline I was speaking with him about the red card. I always believe in my team and I just said how much I trusted us to win the game. And I was right, we did win."
Luiz played a pivotal role in Paris St-Germain winning the match as he forced the game to go into extra time with his stunning header in the 86th minute.
However, despite saying that he would not celebrate if he were to score during that match, Luiz was unable to control his emotions when he netted in the equaliser.
"Chelsea are normally strong at set pieces so you do not expect to score against them like that, but just because they conceded from corners, it does not mean they are not strong anymore," he said. "Chelsea are an amazing club, who gave me many things during my time in England. But now I am a Paris player and I am very happy to be here and into the next round of the Champions League. It was amazing, the spirit, the players gave everything. When we lost Ibra we said we had to keep it simple."