The Lord of the Rings star recently revealed that he is a fan of the Spanish giants, but hit out at Mourinho's style of football and recent behaviour on the touchline.
"I like football to be played on the floor, colourfully, enthusiastically and artistically, and Mourinho does not seem to be a fan of that kind of game, so I have a different approach from him as a fan," the 53-year-old told Sportyou.
"It is little comfort to me that Mourinho's behaviour goes against the tradition of Real Madrid," he added.
"I would like him to be educated, not going to the locker room while playing to spite others, and not sticking his finger in people's eyes.
"It is cowardly to make that offensive gesture towards Tito Vilanova, a polite guy, and not towards Simeone, who would have kicked his a**e."
Real Madrid lifted this season's Spanish Super Cup at the expense of rivals Barcelona through the away goals rule.