The housekeeping manager at the Essex House coldly admitted yesterday that he drunkenly strangled and tried to rape a resident of the luxury hotel and condo two years ago.

Derrick Praileau, 31, pleaded guilty in Manhattan Supreme Court to first-degree murder. He’s to be sentenced June 17 to 23 years to life in prison.

He told cops that he skulked around the building in September 2009 hunting for a victim.

He wound up strangling and stabbing Andree “Sara” Bejjani, 44, president of a real-estate investment firm based in Dubai, in September 2009.

She’d just moved in a month earlier.

When the judge asked how he killed Bejjani, Praileau said, “Strangulation.” He also said he “held her down” while trying to rape her.