The German 1-2 finish also gave them the teams gold medal.
It was just the second four star event for the black mare Classic Moet and Price was chuffed.
"But when you get that close to the medals you can't help but think of what could have been," she said.
However the knowledge that the horse has plenty of improving to do buoyed her.
"I came here hoping for a respectable performance....and never dreamed she would finish fourth. This is the highlight of my career."
The world's leading riders will reassemble in a few days for the Burghley four star event, won last year by New Zealand's Jock Paget, only for his horse, Clifton Promise, to fail a doping test, for which he was later cleared of involvement.