Japan sealed victory in the bronze medal match, winning 5-3 with Muirhead’s last stone not enough to clear Japan from the house.
It leaves Team GB without a curling medal despite being among the favourites.
Defeat to Sweden in Friday’s semi-final saw Muirhead, Anna Sloan, Vicki Adams and Lauren Gray fall into the battle for bronze, which they won at Sochi 2014.
But the quartet were unable to replicate that at a second successive Winter Olympics as Japan capitalised on errors from Muirhead in the ninth and 10th ends to win 5-3.
Muirhead’s last stone was designed to blow Japan away and seal victory, but it wasn’t good enough and ended any hopes of extra ends.
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She attacked with a risky manouver and paid the price.
BBC commentator said: “Eve Muirhead kicks one of the stones in frustration as she leaves the ice. That’s got to hurt. Maybe not as much as coming fourth, though.”
Four-time Olympic curler Jackie Lockhart said: “I’d have liked to see a lot more aggression from the beginning from GB. There was a chance to take the two there with the final shot, but it was such a difficult shot for Eve Muirhead.
“They had high, high hopes of coming here and going home with a medal, but sadly, they go home with nothing.”
A tense, tactical encounter ensued, but Japan blanked the sixth and seventh ends to retain possession of the hammer and took the initiative.
A fine shot by Japan skip Satsuki Fujisawa piled the pressure on Muirhead in the ninth, but the 27-year-old missed her attempted takeout.
Britain had the scoring stone as Muirhead threw the last stone of the 10th end, but instead of scoring two points for the victory – or even one to force an extra end – her shot pushed a Japanese stone further into the house to seal defeat.
The loss means Britain will finish the Games with a record five medals. Snowboarder Billy Morgan earlier on Saturday won the record fifth British Winter Olympics medal, with bronze in the Big Air event.
“The shot was there and we went for it,” Muirhead said. “As a skip it’s hard when you miss the last shot. I’m really proud of the girls – we’ve given it our all this week.
“It’s hard to say we are going home with nothing. We battled hard but I’m devastated we’re going home without a medal tonight. It was a very patient game and it was simple. We went out there and played it simple.
“We had control in the last end – we had hammer but unfortunately it didn’t turn out. It will take a lot of time to let it sink in because you practice that last shot day-in-day-out.
“Of course it’s very difficult when you’re training hard and putting in a lot of hours. But the Olympics is a hard gig. It’s difficult. We all played our hearts out – we left nothing out there. Japan played well and unfortunately it just wasn’t to be.
“We will come back as a team much stronger. I’m absolutely devastated. I am gutted for myself and my team. But at the end of the day we played the best that we could but I’m just sad we couldn’t do it for Team GB. I’m glad we made that medal tally but I’m upset we couldn’t add to it.”