Ukraine-born Olga Butkevych, who received her British passport only in May, has been labelled a "Plastic Brit" - an overseas athlete brought in to raise British medal chances.
Britain's host-nation quota of three wrestlers was cut to one before the Games because its athletes fell short of the qualifying criteria. Their failure drew criticism in the British media because the sport had received 3.5 million pounds ($5.48 million) of funding over eight years to raise standards.
An emotional Butkevych, 26, apologised to the home fans in the packed wrestling arena after her medal chances slipped away in the dying seconds of her first bout.
"I'm so upset. I still don't know what happened. My body was shaking more and more," she said after the six-minute match. "I felt it was definitely my match and I should have won, but that's sport."
Butkevych came to Britain five years ago to work as a sparring partner for the country's wrestlers and decided to stay.
Critics say bringing in foreign-born talent discriminates against homegrown athletes and goes against the spirit of the Games.
The wrestler argued that her situation was not unusual in the modern era of mass migration. Other foreign-born British athletes include the U.S.-born hurdler Tiffany Porter and 400m runner Michael Bingham, also born in the United States.
Butkevych made a bright start against Ecuador's Lissette Alexandra Antes Castillo, tying the first round and winning the second. But it all went wrong in the third and final period when the Ecuadorian bundled the Briton to the edge of the mat and scored the winning points with seconds to spare.
There had been hopes of a British wrestling medal after Butkevych came second in a test event in December. Noel Loban won Britain's last Olympic wrestling medal in 1984.