Robson and Murray made it to the final last year before losing to Spain
Great Britain's hopes of winning the Hopman Cup ended with defeat for Andy Murray and Laura Robson in the decisive mixed doubles rubber against France.
Nicolas Mahut and Kristina Mladenovic won 6-4 6-2 to give France the tie 2-1.
Robson had earlier lost the opening singles rubber 6-4 3-6 6-0 to Mladenovic, before Murray battled past Mahut 7-6 (7-3) 7-6 (7-5).
Britain will take on the United States in their last Group B match on Friday but cannot now qualify for the final.
The Americans have won both their ties so far, while Britain have a 0-2 record after losing to Italy in their opener.
Robson, 16, had been defeated in straight sets by French Open champion Francesca Schiavone on Monday but made a strong start against 17-year-old Mladenovic with an early break.
I don't think we played too badly, I thought they played really well
The pair had met twice before in the juniors, with one win apiece, and the 5ft 11in Mladenovic came storming back with some excellent serving and heavy groundstrokes to take the first set.
Robson cut an increasingly frustrated figure as she saw four break points slip by in a 13-minute game at 2-1 in the second, and a 0-40 lead disappear at 4-3, but after Mladenovic went long on the fourth break point of the game it came down to a deciding set.
Robson could not complete the comeback, however, and Mladenovic stormed through the final six games to wrap up an impressive victory.
The pressure was on Murray to keep his team in the tournament and he made a slow start, dropping serve immediately in the face of Mahut's attacking style.
Mahut served for the set at 5-4 but could not convert two set points from 40-15 as Murray began to find some rhythm on the return, and after breaking back the Scot dominated the tie-break.
An early break in the third looked to have completed the job for the world number four but he then played a sloppy service game to allow Mahut back into the match, and the Frenchman looked the more likely as the set progressed.
But another set point went begging for Mahut and Murray again made him pay in the second tie-break, letting a 5-2 lead slip before closing out the match with a couple of fizzing passing shots.
"There was a big contrast in styles with his serve-and-volley setting up a lot of passing shots and short sharp rallies, but it was a really, really fun match," said Murray.
It came down to the mixed doubles and a heavy fall for Mahut at deuce in game three did not bode well for the French, but after getting his ankle taped he came straight out and helped force the first break on Robson's serve.
The French pair served out the set and, after losing a 2-0 lead at the start of the second, regained the advantage in game five thanks to some blistering hitting from Mladenovic.
Britain reached the final 12 months ago but their hopes of going one better effectively ended when Robson dropped serve again and Mahut served out confidently to set up a crunch match on Friday between France and Italy.
"I don't think we played too badly, I thought they played really well," said Robson. "We had a tough one on Monday so hopefully we can win one on Friday."
Asked how he was feeling after two matches in quick succession, Murray said: "I'm a little bit stiff and sore but that's to be expected, I've been off court for five or six weeks and the body's feeling it a little bit."
The US earlier beat Italy 2-1 after Bethanie Mattek-Sands stunned world number seven Francesca Schiavone 6-4 6-4, and John Isner beat Potito Starace 7-6 (7-5) 4-6 6-4.