The GB skip got off to a bad start in the first end when she missed a take-out after her stone deviated on the ice after going over the bit of debris, which allowed the Canadians to manoeuvre themselves into a two-shot lead.
Perhaps more significantly, Canadian skip Jennifer Jones stole one more on the next end to ask early questions of the British rink to which, ultimately, they had no answer.
There was some pressure on Jones in the final throw of the game with Canada winning 5-4 but she was unerring in her draw to increase the margin of victory and take her team into Thursday's final against Sweden, who beat Switzerland in the other semi-final in the Ice Cube Curling Center.
Muirhead claimed bad luck was the last thing she needed against an in-form Canadian side who have won every one of their 10 games in Sochi so far.
" I'm gutted and the girls are gutted as well," said Muirhead.
"I just don't think that the curling Gods were with us.
"That first end, that pick-up was brutal.
"It was a hair from one of the brushes, it just caught the stone.
"There is nothing you can do when a you get a little bit of debris on the ice but losing a two from something that you can't control against Canada, it's going to be tough to come back.
"We did come back but anything we left them, they made today. Sport is tough sometimes, sport can be brutal and that proved that it was tough."
Muirhead acknowledged that the Canadians were at times relentless.
"You feel like your back is up against the wall," she said.
"But we were giving it back to them. It was a high quality game.
"We can't be too harsh on ourselves. We're a young team, we have a long future ahead of us and a lot of countries know we are here and will still be fighting.
"Our form was good and we played well as a team. I'm gutted but I think we gave it everything.
"But Jennifer played well, they all played well. We knew it was going to be tough. Good luck to them in the final.
While disappointed at missing out on the chance to win gold - the last time a British women's team managed it was in 2002 - Muirhead vowed to take a bronze medal back from Russia.
"We still have a chance for a medal," she said.
"We have trained hard for a medal so we'll give it our all.
"We'll go in to give it 110 per cent because, believe you me, I don't want to go home without a medal round my neck."
Coach David Hay tried to put the stray hair into context.
"It takes very little for these type of stones to deviate off the line," he said. "It didn't miss by a fraction, it missed by a country mile.
"It is similar to a kick in snooker or a bad bounce in golf, it is one of those things and you have to put up with that.
"But they played really well and I am proud of them.
"The first thing they said in the changing room was, 'we are going to get that bronze tomorrow'."
Jones revealed the pressure she was under with her last shot, which had to be pin-point in its accuracy.
She said: "You can feel it but that's what you trained for and, to me, that's what makes sport so exciting, getting that adrenaline rush.
"We've had to make some big shots before and so we knew how to deal with it.
"I knew it was close when I felt it go. That's a great feeling.
"It's crazy. We have worked so hard and to have it all come true and be in that gold medal game, the game you have dreamed of for your entire life. To make a big team shot to win. You couldn't have scripted it any better."