Scotland took on Sweden in the Page 3v4 play-off in Beijing on Saturday looking to secure a place in the evening semi-final game against Russia.
But it was not to be as they fell to a 8-5 defeat to their opponents, leaving them to play for bronze in Sunday's medal match against the loser of Russia versus Sweden.
It was a tight affair though with Sweden taking the early advantage with a single steal in the second end for a 2-0 lead when Muirhead's final tap-up attempt did not come off.
The teams then swapped singles for the next three ends as Sweden led 3-2 at the break.
That was extended to 5-2 after the sixth end when Sweden skip Anna Hasselborg hit out a Scottish stone to score two point points.
Muirhead replied with two in the seventh to reduce the lead to one but any momentum gained was swiftly lost when Sweden scored three points in the eighth.
And following a Hasselborg double take-out, Scotland could only hit for one point in the ninth to take the score to 8-5 in Sweden's favour, after which the Scots ran out of stones in the tenth end.
"We're disappointed. You don't want to lose a play-off game, but Sweden were the stronger team," said Muirhead.
"We battled hard but we gave her [Anna Hasselborg] too many half-shots and we didn't have many. So, we've just got to dust ourselves off and come out firing tomorrow. We've still got a chance for a medal.
"We've got to take the positives out of that, going into tomorrow. It's hard but as a team we've done it many times. I think about the medal at the Olympic Games after losing the semi-final."
"We've got to keep our heads high, we've played well in these last few games to get ourselves into this position."
Read the original article on Eurosport: Muirhead's Scotland left to battle for bronze after Sweden defeat