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Donna Jou, of Rancho Santa Margarita, disappeared nearly two years ago after answering an ad placed by Burgess on Craigslist.
Burgess told a packed courtroom Wednesday he brought Jou to his Palms area home in June of 2007. He admitted to giving the 19-year-old alcohol and drugs, including heroin and cocaine.
Burgess says he panicked when he woke up and realized she died of an overdose, and dumped her body in the ocean.
"In the morning I woke up and she was gone -- she was dead," said Burgess. "I panicked and got scared and made a really bad decision. I went down to my sailboat and I gave her to the sea."
Burgess agreed to meet privately with the woman's parents at LAPD Headquarters.
"[Reza and Nili Jou are] very relieved that Mr. Burgess has admitted his role in the death of their beloved daughter," said Gloria Allred, the family's attorney. "They have a lot of questions for him and want to know exactly what happened to her."
Jou's body has never been found. Allred said Wednesday her parents are still hopeful her body can be recovered so they can bury her remains.
"I miss her so much. I am very devastated. I love my daughter very much," said Reza Jou, the victim's father.
Burgess is expected to be sentenced to five years in prison on May 18.
Jou was an honors student at San Diego State University.
The Associated Press contributed to this report.