Hazelmary and Peter Bull refused to let civil partners Steven Preddy and Martyn Hall stay in a double room at Chymorvah House in Marazion in Cornwall in 2008.
The couple, who had already lost cases at Bristol County Court and the Court of Appeal, said they were "saddened".
Mr and Mrs Bull have said they regard any sex outside marriage as a "sin".
The Bulls denied discriminating against Mr Hall and Mr Preddy, who are from Bristol.
Sixty-nine-year-old Mrs Bull and her 74-year-old husband said their decision was founded on a "religiously-informed judgment of conscience".