Carvalho, 32, ended a six-year spell at Chelsea to reunite with Mourinho at the Bernabeu this summer and, while the team got off to a disappointing start with the 0-0 draw against Real Mallorca, he feels there is no doubt Madrid will succeed this season.
"He is the best coach in the world, a coach who knows exactly what needs to be done," he said. "I have known Jose for many years now and I know the way he works."
Carvalho believes Madrid showed they are solid at the back in their opening game and fully expects them to take three points when they host Osasuna this weekend.
"Our defence played with great confidence but it was a shame we couldn't capitalise on our chances to score," he said. "We are going to give our best performance to win against Osasuna on Saturday in order to earn our first victory of the season."