The Netherlands won team showjumping gold at the World Equestrian Games as Britain's last remaining rider, Scott Brash, pulled out of the event.
World number one Brash would have begun the day in 36th place but he and the GB team decided it was "a lot of ground to make up" on board Hello Sanctos.
A 25-year-old dentist from Kinross, Joanne Eccles, is now Britain's only remaining world title hope in Caen.
Eccles leads the vaulting contest with one day of competition remaining.
She is defending a title she won at the last World Equestrian Games, four years ago, in a sport which involves gymnastic manoeuvres on the back of a moving horse.
"I feel really comfortable in the arena. I love it and I'm having fun," Eccles told BBC Sport.
Britain's showjumpers won Olympic team gold in 2012 so failing to reach Thursday's world team final came as a shock, with 28-year-old Brash the only Briton to make the top-50 cut for the next stage of the individual contest.
A statement from the team read: "There is a lot of jumping still to do in the individual qualifying competition; a lot of ground to make up in the leaderboard and the likelihood of qualifying for the individual final, with the standard of jumping here this week is not likely.
"With the horse in mind and looking ahead to the forthcoming Nations Cup in Barcelona, next year's European Championships and beyond, the decision has been made to withdraw the horse from further competition this week."
British equestrian chef de mission Will Connell added in his blog: "We are missing some of our big guns here and some of the horses we did have here, whilst super talented, are lacking championship-level experience.
"So we have not achieved the much-valued Olympic qualification in jumping so the team will have to perform at the Aachen Europeans in 2015."
London 2012 silver medallist Gerco Schroder, riding Glock's London NOP, had one fence down as the final rider in the team jumping final but did enough to secure gold for the Netherlands, whose combined score of 12.83 beat hosts France (14.08) and the United States (16.72).
Those three teams earned qualification for Rio 2016, alongside Germany in fourth and sixth-placed Sweden (Brazil, in fifth, having automatically qualified as the next Olympic host nation).
The individual medals will be decided on Sunday, following a final qualifier on Saturday.