Muirhead, alongside Anna Sloan, Vicki Adams and Claire Hamilton, had a nightmare start after some debris on the ice forced her stone to pick, meaning she surrendered a soft two that gave Jones a flying start.
Canada are unbeaten at these Games and made their advantage count, though the match wasn't decided until the final stone, Jones securing a 6-4 win that sets up a final with Sweden, while Muirhead's rink now play Mirjam Ott's Switzerland for bronze
"The curling Gods were not with us," admitted Muirhead.
"That pick up in the first end was brutal and losing a two off the bat from something you can't control against Canada, it was going to be tough. There is nothing you can do when you get debris on the ice.
"I'm gutted and so are all the girls. I came into this tournament saying I wanted no regrets and we gave everything we could in that game.
"I'm proud of the girls and we've still got a chance of a medal. I don't want to come away without a medal around my neck.
"Our backs were against the wall but we gave it back to them and it was a high quality game. We've trained hard for this and we'll give the next match our all."
Muirhead's rink lost to two-time Olympic silver medallist Ott in the round robin stages but coach David Hay backed them to bounce back and win Team GB's first curling medal since Rhona Howie's gold in Salt Lake City 12 years ago.
"The girls played their best game of the week and I'm proud of them but bitterly disappointed to lose in that sort of way," he said.
"The first thing they said afterwards is we're going to get that bronze now.
"You don't want to get a start like that, we got a pick in the first end and gave them the softest two of all time and a couple of slack shots in the second end forced us to give up one."
� Sportsbeat 2014
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- Vicki Adams