He has already posted a tongue-in-cheek message on Twitter saying 'Gary Neville I love u', which did not provoke a response from the pundit.
Luiz, 24, said: "I know Gary Neville in the past was a very good player but he sometimes needs respect.
"Gary Neville say bad, other people say good. I just need to show with my work on the pitch. I respond like this.
"When Gary Neville say this, (he) don't respect me. Now that the stats show I am up there among the best.
"I just know that in all the games that I am on the pitch, I just try to show my best ... I work a lot, tackle, I give my heart on the pitch."