Javier Turienzo Alvarez awarded two disputed penalties to Racing and sent off two Real players in the final 17 minutes, which deprived the nine-time European champions of a provisional place at the top of the table.
Raul had given Real a first-half lead.
"I have received more than 50 phone calls at my house with death threats against me and my family," Turienzo Alvarez said in an interview with Punto Radio.
"I have a daughter of six years old who returned from the park yesterday crying. She said: 'the children tell me you ruined things for Real'... and it hurts me to the core."
Turienzo Alvarez said media coverage of the game had contributed to the hostile atmosphere towards him.
"I don't want to apportion blame but a newspaper front page on Sunday was hurtful with a picture of me in a target and a message 'go for him.' I don't think this is fair," he continued.
"When I left the hotel on Sunday some 30 or 40 people crowded round the car threateningly with the newspaper in their hands saying bad things. One day something will happen and then everyone will be sorry."
The referee also defended his profession from accusations of partiality.
After Saturday's game, Real's sports director Predrag Mijatovic was critical of referees, saying: "We are very angry. Some very strange things have happened and mistakes that cannot be forgiven. It isn't normal that they do what have done to us."
Turienzo Alvarez said: "There is nothing strange going on. Everyone makes mistakes from players, to directors, to referees."
On Tuesday, Real Madrid issued a statement on their Web site (www.realmadrid.com) condemning the threats against the referee.
"We consider it intolerable the criticisms of a particular refereeing performance, that could be perfectly legitimate, can be converted into insults and threats that affect not only the referee but more seriously his family," said the club.
"These attitudes are completely unacceptable and are not shared by Real Madrid."
