The Brazilian international made his fourth appearance of the season on Tuesday during the Blues' 2-0 win at Swindon Town in the Capital One Cup.
"I don't need to prove anything," BBC Sport quotes Luiz as saying. "Everyone knows who David Luiz is.
"I want to play football and enjoy myself on the pitch so when I have an opportunity to play, I want to enjoy just that."
Luiz recently claimed that he rejected the chance to join Barcelona over the summer in order to stay at Stamford Bridge.