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Mike Etherington-Smith, chief executive of British Eventing has told ITV News that "because it was so close, there is a bit of frustration - but we got a silver medal."
Zara Phillips said being presented with her Olympic silver medal by her mother, the Princess Royal, was "amazing".
Phillips, who became the first member of the royal family to win an Olympic medal said the medal win was "huge".
The Queen's granddaughter said: "It's amazing, obviously."
"We wanted the gold but to get an Olympic medal is incredible anyway.
"We've had an amazing week, it's been a great, an unreal competition and when you get one of these put round your neck it brings it back to you and you realise everything was worth it."
Princess Anne presented medals to the three winning teams - Germany, Britain and New Zealand - in the centre of the show-jumping arena as the Chariots of Fire theme played in the background.
Phillips could be seen mouthing "oh man, oh man" as her mother began presenting medals to Team GB.
She beamed and kissed Princess Anne, who is herself a former Olympian, on both cheeks after receiving her medal.
The whole crowd were on their feet when the British eventing team arrived to be awarded their silver medal and joining in the cheers were the Duke and Duchess of Cambridge, Prince Harry and Princess Beatrice.
The royals have been well represented throughout the eventing competition and were there to see cousin Zara Phillips awarded her silver team medal by her mother the Princess Royal.
Mary King knocked the same two fences as Kristina Cook adding 8 penalties and leaving her with a final score of 50.1 in the individual jumping final.
Kristina Cook has had 8 penalties in the individual eventing jumping final and will miss out on a medal.
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I watched their every move - through all three telling, testing and beautiful disciplines. Meeting them I glowed with pride.
The equestrian team have won a team silver in the three day eventing, narrowly missing out on the gold medal