With one rider to take to the showjumping course, New Zealand had a chance at claiming a silver medal, with just 4.1 penalty points separating themselves in fourth, and second-placed Australia.
However, New Zealand's world number two-ranked rider Tim Price, on Vitali, dropped three rails in his round to eliminate the team from medal contention.
As it happened, the team's French and Australian rivals both went clear in their rounds on the course, so even a perfect performance from Price would have come up short.
The New Zealand team eventually finished in fifth place, behind Great Britain, Australia, France and Germany.
The Great Britain team of Oliver Townend, Laura Collett and Tom McEwen comfortably claimed the gold medal after capitalising on fine performances in the dressage and cross-country - their riders copped just eight penalty points in the showjumping to give the side a 13.9 point victory over the second-placed Australian trio of Shane Rose, Kevin McNab and Andrew Hoy.
While all three New Zealand riders also progressed to the individual-eventing final round, they failed to make an impression with Jonelle Price finishing highest of the trio in 11th place.
Jesse Campbell finished in 22nd place, while Tim Price ended his campaign in 24th after another penalty-strewn round.
Then, riding just before the French team's number two and under extreme pressure, Jonelle Price produced a perfect round, drawing on her wealth of experience in the sport.
"This is all about pressure jumping and he [her horse] did that today," Price told Sky Sport.
Perhaps that performance put some pressure on Frenchman Karim Florent Laghouag, as he dropped a rail on his round on the course to close the gap between the two teams - and third and fourth place - to less than one rail.
Australia was also just 1.3 points ahead of France at this stage, setting up an exciting finale to the event as each country's final rider determined the last two medals on offer.
First of the three was New Zealand number one Tim Price and his young charge Vitali never quite looked comfortable on the course, the pair dropping two rails at the first triple obstacle.
One further dropped rail meant Price finished with 12 penalty points, pushing the team below Germany in the overall rankings.
A disappointed Price told Sky Sport his horse's youth really showed under the pressure of the event.
"He's a young horse and that was, possibly, on display a bit tonight," he said about Vitali.
"We're all here trying our hardest, they're not machines, they're animals and you've got to take it with a grain of salt if it doesn't go to plan.
"Very disappointing because the other two guys - Jesse and Jonelle - jumped out of their skins and it's a shame to let them down."
