Ngamba, who was born in Cameroon but sought safe haven in Britain aged 11, was beaten by Panama's seventh seed Atheyna Bylon by split decision in the semi-finals of the women's 75kg category.
That denied her a place in Saturday's final but boxing hands out bronze medals for losing semi-finalists.
The Refugee Olympic Team first competed at the Rio 2016 Games and is designed to represent forcibly displaced people worldwide.
There are 37 athletes competing for the team in Paris from more than a dozen countries.
The 25-year-old Ngamba is a lesbian, which is illegal in her native Cameroon.
She qualified for the Olympic competition by right and won two matches in Paris to reach the semi-finals.
Ngamba had trouble dealing with her taller Panamanian opponent but continued to attack throughout the match.
She was behind on points after the first round but came back in the second, leaving it all to fight for in the final round.
Bylon had a point deducted in the third round but the Panamanian still did enough to get the win, much to the displeasure of the crowd at Roland Garros, the home of the French Open tennis tournament.
After moving to Britain as a child, Ngamba had a tough upbringing, bullied at school for her poor English and her weight.
She took up boxing and qualified by right for the Olympic competition.
Britain wanted to select her for the Paris Games and boxing officials appealed unsuccessfully for her to receive a British passport.
