The youngster has been eased into the Blues' first team in his first season at Stamford Bridge, sometimes playing in midfield instead of centre-back, and admits that his boss is not an easy taskmaster.
"Mourinho puts pressure on all his players. It is very demanding - he wants perfection from everyone," the Frenchman told L'Equipe. "He won't let you take a month to fix something.
"In defence, he asked me to move tactically, to be well placed to listen to the older players around me, John [Terry] and Gary Cahill.
"Initially, in midfield, I was obsessed with the ball - I was not paying enough attention to the players behind me - but it's something I've been working on. In midfield, it's different. He asks me to use my power and stay in place to help the defence.
"[I've learned] to hate losing," the 20-year-old continued. "The only thing you get when you lose is the right to eat in the evening. When we play at Chelsea, we should not accept losing."
Zouma is winning over the fans at Stamford Bridge but feels that he has a long way still to go, particularly if he wants to secure a place in the France squad when they host Euro 2016, and the former Saint-Etienne man knows that displacing one of Terry and Cahill may be necessary.
"It's good to see that [the fans] know my name now," he remarked. "Maybe my physicality impresses them a little, yes, but it will have to stay impressive throughout my career, otherwise it is useless.
"I know that we are talking about me but I really have to be very careful with that because it can play tricks on you. Anyway, I was taught not to get carried away with myself - if I did, I'd get a thrashing.
"Honestly, I think I have to play a little more [for Chelsea to make the France squad for Euro 2016]. We have many, many players in contention to be worthy of such an event so I'll make a big effort.
"It's normal [that Cahill and Terry like to play together] - I also like to play with them. They're really beefy, they have the experience, but, when you have a goal, do not look at who is in your way. You have to fight, that's all."