Sarri's position is precarious after a run of poor results, but the 60-year-old Italian showed some tactical flexibility and his team put in a valiant performance in Sunday's Carabao Cup final with Manchester City, who had beaten the Blues 6-0 just two weeks earlier.
City retained the trophy with a 4-3 penalty shootout win at Wembley, but the match was overshadowed when Kepa declined to go off, sparking an angry response from Sarri.
Both parties later played down a misunderstanding and Luiz was adamant the players are on Sarri's side.
"The coach has the power over the group. He has our respect," Luiz said. "For me, there is not a problem here for that. We all believe in his philosophy, we all believe in the way he wants us to play.
"That's why we did a great game against the best team in Europe at the moment.
"Apart from that, it was a misunderstanding and we all want to do what is best for Chelsea."
Former Chelsea midfielder Michael Ballack believes the Chelsea hierarchy need to take a strong stance on the matter, to support Sarri.
"It was not a good picture for Chelsea," Ballack said. "The board has to say something because it is really, really important that the players respect the coach and respect each other. Something shouldn't happen like that."
Luiz was the closest player to Kepa as Sarri readied Willy Caballero to come in the final minute of extra-time, with the fourth official's board even indicating Kepa was to come off. Caballero saved three penalties in City's 2016 League Cup win over Liverpool.
Rules dictate a player has the right to refuse to be replaced and referee Jon Moss took time to clarify the incident before Kepa stayed on for the shootout.
He saved from Leroy Sane, but dived over Sergio Aguero's effort and Jorginho had a penalty saved and Luiz hit the post as Sarri's wait for a first trophy of his career goes on.
Luiz added: "It is never easy for us to listen from afar. I didn't know if the coach wanted to make the change because it was his decision or because he (Kepa) had already been on the floor twice.
"Kepa was saying 'no, I'm good, I can stay on the pitch', but from far you can't understand.
"I'm sure if Kepa knew the coach wished to change him because it was his decision, he would have come off because he is a great professional, he is a great boy and would respect that."
Chelsea's senior players did not mediate on the issue, with Luiz staying by Kepa and captain and right-back Cesar Azpilicueta on the far touchline to Sarri's dugout.
Put to him that the senior players should have cleared up the situation, Luiz insisted he could not leave his position, even though there was a break in play.
He said: "I cannot move there - then the ball comes, we concede a goal and you say to me 'I'm not in my place'.
"The game was stopped but the referee was saying 'play, play, play'. The referee went there and said 'okay no more substitution', came back and we restarted."
Former Manchester City boss Stuart Pearce described the incident as a "show of petulance" from Kepa and feels the images contradicted the explanations which subsequently emerged from Chelsea.
Pearce said on talkSPORT: "It undermined him (Sarri) and made it look an absolute shambles.
"His reaction didn't go with the the story that has come out from Chelsea, that it was a misunderstanding.
"The question people ask is has he lost his players. No - it was only one individual that acted very, very childish, and should have just said 'thanks very much, OK, fine, my race is run today'.
"And Willy Caballero has a good penalty shootout ratio. He might have been sat there thinking I'm making this substitution not for the injury."
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