Real were held 0-0 on Sunday while arch-rivals Barcelona swept aside Racing Santander 3-0 opening up an immediate two point lead in the La Liga standings. The champions only dropped 15 points on their way to the title last season.
"I am a coach not Harry Potter," Mourinho told sports daily AS in an interview on Wednesday.
"He is a magician. Magic is fiction and I live for football which is real. I've only been two months in Madrid. Do you know how many training sessions I have had with everyone together, including the new signings? Not even 10."
Last season's treble-winning coach with Inter Milan was brought in to replace Manuel Pellegrini, in an attempt to end a run of two trophyless seasons at the Bernabeu and to break Barcelona's dominance of La Liga.
"My profile as a coach is different to those they have had in recent years," he added. "If things go badly and I have to leave... I would have one of the best clubs in the world waiting for me.
"This personal stability allows me to say I am the ideal person to be at Madrid because I fear nothing. Madrid need stability and I'm here to give it.
"Madrid is in many ways a conflict of footballing ideas. Coach after coach after coach... They need stability."
Mourinho signed a four-year contract in May to become their tenth coach since Vicente del Bosque was sacked in 2003.
Chelsea win again, Real Madrid start with draw
Mourinho convinced Ozil to join Real Madrid
Special One Mourinho is Real key to ending Barca reign
Harry Potter's 100 million pound goodbye
No rift with Mourinho, says Casillas