Wenger stated he was "embarrassed" for Mourinho, who described the Gunners boss as "a specialist in failure" following the Frenchman's comments that the title was Chelsea's to lose and anyone playing down their title hopes was doing so out of fear of falling short.
Mourinho has repeatedly played down Chelsea's title chances this season, his first since returning to Stamford Bridge.
Luiz, who was speaking at Pepsi Max's 'The Art of Football' event in London, said: "We are top of the league now, we are happy with this.
"We keep working hard every day for our job. Of course, I respect everyone, other teams, but we need to do our job. That's it.
"We cannot listen to everyone, because if you listen to another coach, Chelsea don't have just one coach, Chelsea have 10, 20, 100 (coaches)... everyone wants to be part of our club. And that's natural."
It has been suggested Mourinho is at his most outspoken when he wishes to deflect attention away from his players, but Luiz is unfazed and believes Chelsea's players should relish the responsibility which comes with leading the Premier League with 12 games to play.
"You don't need to take pressure off me, because I love pressure," the Brazil defender added.
Luiz is enjoying life under Mourinho.
"He has a great ability to work," the 26-year-old said.
"I'm a guy with an open heart. I want to learn every day. I'm happy with this, I'm happy when I can play for a big club and have an opportunity to work with a good coach."
Eden Hazard is also thriving under the Portuguese, who recently lauded the Belgian as the world's best young player.
Luiz suggested his 23-year-old team-mate could go on to become the best on the planet at every level.
"He can be one day the best player in the world," Luiz said.
"I'm so happy for him, because he's a great person, a great guy, with a lot of talent."
Luiz is one of six footballers - along with Lionel Messi, Robin van Persie, Jack Wilshere, Sergio Aguero and Sergio Ramos - featuring in a bespoke art collection celebrating the artistry of football.
He was happy with his portrait, created by Brazilian artist Ricardo AKN.
He said: "I was so anxious to get the results. It's amazing.
"When you have this great idea to mix the world of art and world of football together, you get amazing results. I'm so proud to be part of this project."
The six players are hoping to star in the summer's World Cup and Luiz hopes the hosts will come out on top.
"I want this guy to celebrate at the end," he said, referring to his portrait.
"It's my dream come true if I can go to the World Cup. I was young and I saw two, three days ago pictures of me watching TV in a Brazil shirt.
"Now I can be inside the screen and make the world happy with my football.
"It's a great opportunity for our generation, because we can win and can make history."
England's opening game with Italy on June 14 is in the Amazonas city of Manaus, where Roy Hodgson is visiting this week.
Luiz compared the anticipated stifling heat with Brazil playing in a cold climate and warned England they must adapt to have a successful tournament.
He said: "This is the World Cup. If you want to win the World Cup you need to win in all the circumstances. You cannot choose.
"Like for Brazil to play in one country so cold, you need to adapt. That's natural. Football and players need to adapt all the time."