The Blues needed a win to keep their title hopes alive and produced a battling display to come from behind to secure the three points. Luiz played a key role as he served up a solid defensive effort and also bagged a goal - but he arguably should not have finished the game after escaping a second yellow for what appeared a blatant trip on Wayne Rooney.
As well as demonstrating class in abundance, Luiz has shown an uncompromising nature to his play since his January transfer to Stamford Bridge and Ancelotti feels the Brazilian may need to rein himself in.
"Luiz has to understand English football and be more calm on the pitch," Ancelotti said. "With more experience of the game here, he can change his behaviour.
"As an attacking force, he has been fantastic - as he proved when he scored on Tuesday - but, defensively, he needs to improve that side of his game."
Sir Alex Ferguson has been charged with improper conduct for his comments towards referee Martin Atkinson as he was incensed that Luiz was not sent off at Stamford Bridge.
Ancelotti said: "I know Sir Alex had an argument with the referee, but I don't want to comment.
"I have a fantastic relationship with Sir Alex and we spoke after the game. He was disappointed about the decisions of the referee but this is football - one coach will be happy after a game like this, the other one unhappy. We spoke briefly about this, but then about other things.
"After a game you are not cold. You have all the emotions of the game. Sometimes you will speak about decisions. This is normal, I think."