Germany clinched their sixth successive team dressage gold medal as Great Britain lost their hold on the bronze medal position on Saturday.
A brilliant ride by Ulla Salzgeber on her horse Rusty took Germany clear of the field.
Spain won the silver medal, while the USA pipped the Netherlands for bronze.
Unfancied Britain ended day one in third after excellent rides by Carl Hester and Emma Hindle, but the team finished the competition in seventh.
The Netherland's Sven Rothenberger, with Barclay II, had the chance to leapfrog the USA with their last ride, but his score of 69.833 came up just short.
Britain's Richard Davison and Nicola McGivern finished with scores of 68.542 and 66.458 respectively.
"It was very disappointing," said GB team leader David Trott.
"We always knew it was going to be a hard day but we didn't quite get the performance we wanted.
"Richard produced a sound test but we were hoping for more from the final combination and in the end they were well below their potential.
"But all credit to Spain. Their girl really put together an outstanding test and is now in the silver medal position, so it shows how strong she was.
"On the positive side we have three through to the individual and that is very pleasing."
The event doubled as the first of three rounds for the individual dressage medals, which will be decided on Wednesday.
The top 25 riders - including Hester, Davison and Hindle - progress to the Grand Prix Special on Monday, with the top 15 from that competition taking part in the freestyle round, where competitors perform their own routine to music.