Derek Brown, British Curling's performance director, stood by his team and insisted they were closer to qualification than the standings suggest.
Team hope for future of women's curling
"They have performed pretty well and lost a couple of games in extra ends," he said.
"We are ranked seventh in the world and we came in here with realistic expectations.
"Eve has played some fantastic games and missed some key shots as well, but she is a fantastic young talent and we firmly believe that we had the best four players out on the ice."
The first of several mistakes in the match from Muirhead, in the second end, saw a regulation shot slide through the house, miss an unguarded Canadian stone and hand their opponents an unexpected lead.
But the 19-year-old found her bearings when faced with a similar situation in the third to give Britain a 2-1 lead.
Jackie Lockhart played two good shots in the fourth, but Bernard made use of the last stone to even up match.
I'm sure lots of shots will haunt me for a long time
On the final stone of the sixth Muirhead's ambitious attempt to slip between two guards, take four points and a stranglehold on the match failed to allow Canada to edge ahead once more.
The skip's heavy final stone in the seventh saw another point slip away and, with the pressure building, a tentative final stone at the end of the eighth failed to draw into the house.
But the youngster shifted the tension onto opposite number Bernard with a fine shot that picked up two points in the ninth.
The Canadian flirted with defeat but her stone held up just enough to concede only one point and take the match into an extra end.
But, as Switzerland's win across the rink ended Britain's hope of progressing, they were also denied a consolation win as the competition's form team put together a clinical final end.
GB women curlers downcast after exit
"I am a bit of a perfectionist on the ice and when little shots don't come off it can bug you," said Muirhead.
"I'm sure lots of shots will haunt me for a long time, but you just have to put that behind you.
"You do feel bad and feel like you have let people down, but I don't think it was too much for me."
The women's semi-final line-up sees Canada take on Switzerland, while Sweden face China with both games starting at 1700 GMT on Thursday.
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