Chelsea manager Mourinho and Arsenal boss Wenger have recently traded words -Wenger said he was embarrassed for Mourinho, who had claimed that the Frenchman was a 'specialist in failure'.
Luiz told Sky Sports News: "Football is like this, you cannot listen to everyone because if you listen to another coach, you don't just have just one coach, you will have 10, 20, 100 coaches. Everyone wants to be part of our club and that's natural."
The Brazilian is also aware of the pressure on the players with 12 games to go and welcomes it, even if Mourinho's comments were designed to take the attention off them.
He said: "I love pressure, you don't need to take pressure of me because I love pressure and that's why I play for a big club - that's why I am here.
"We are not afraid, we are top of the league now, we are happy with this. We keep working hard every day. Of course I respect everyone, every team, but we need to do our job."
Speaking at an event to promote a fusion of of football, photography and art,
Luiz also said he believes Chelsea team-mate Eden Hazard can become the best player in the world.
"He can be Leonardo da Vinci in football - he can one day be the best footballer in the world," he added.
Meanwhile, Luiz admits he cannot wait for this summer's World Cup finals in his homeland.
"If you want to win the World Cup, you need to win in all different circumstances, it is a dream come true to go to a World Cup," he said.
He also insists that England are not complete outsides for the finals.
"The English should believe more, they have a great generation with the mix of young and experienced players," he said.
"Sometimes the English say it's OK to make a quarter-final or semi-final but come on, you have to believe you can do more.
"You have players like Jack Wilshere who is great and can make history for his country.
"I always believe you can achieve anything in life and that's what you should do. If not you can never grow."
He also has little doubt that his Chelsea team-mates Frank Lampard and Ashley Cole should make the trip.
"Frank Lampard and Ashley Cole are both fantastic players and deserve to get there," he said.
"Ashley didn't play so much this season but he works hard every day and it's the same for Frank.
"We talk about the World Cup, of course. Everyone is excited.
"We encourage each other. It's a great opportunity for our generation, not just for Brazilian players but for everyone else as well."