The 48-year-old made the false claims during an interview at his home in Deal in Kent after he was arrested on March 9.
Sitting on his sofa in handcuffs, wearing a white t-shirt and dark shorts, Couzens first claimed not to know 33-year-old Ms Everard when he was shown her photo.
He then said he was in “financial shit” and had been “leant on” by a gang to pick up girls for them.
In footage released by police, Couzens claims he had tried to “rip off” one of their call girls and the gang had approached him during another booking with her at the Burstin Hotel, in Folkestone.
He said they later put pressure on him after turning up at his home address and he just “drove around aimlessly and at random” to find someone.
Couzens said he handed Ms Everard over to the gang, who he said were from the “Bulgaria, Romania Albania” region, near Charing racecourse, in Ashford, Kent.
He said he was pushed against the front of his car and the gang drove off with “the girl”.
When questioned about where Ms Everard was, he repeatedly claimed to not know.
“If I could do something to get her back right this minute, I would,” he said, but added: “I’ll do it again tomorrow if it means saving my family… these guys mean business.”
The footage was played at Couzen’s sentencing today.