The 22-year-old stepped onto the ice for the gold-medal match off the back of five straight wins however she could not add an all-important sixth to defend her European crown.
In a match that saw the lead change hands five times and go to an extra end, Sidorova's rink took the lead in the first before Muirhead played a draw to score two points in the third.
That made it 2-1 however Russia added another point in the fourth and again in the fifth although Muirhead was on top 4-3 in the sixth after playing a draw with her last stone and scoring two.
Sidorova levelled in the seventh and retook the lead in the ninth before Muirhead hit back in the tenth to force an extra end that saw the Russians, with the stone, hit for one point to win 6-5.
That secured Sidorova her first major title and Russia's first European gold since 2006 and Muirhead had nothing but admiration for her opponent, who she beat 6-5 in the round-robin stage.
"It wasn't our best performance, we've played better this week," said Muirhead of her team which included Anna Sloan, Vicki Adams and Claire Hamilton.
"We just missed one or two slack shots here and there but they played well. The last end could have gone either way. Their second made a fantastic double and took out one in the house too."
Meanwhile in the women's bronze-medal match Swedish skip Margaretha Sigfridsson gave the home crowd in Karlstad something to shout about as they beat Denmark 9-3.
Always in control, Sweden led 4-1 at the end of the third end and extended the score to 7-2 in the fifth before the two teams shook hands with the score 9-3 at the end of the eighth.
It could have been a lot better for Sigfridsson as her rink finished first in the round-robin stage but lost the page one-two play-off and then semi-final but she was not complaining with bronze.
"One of our best strengths is that we really lift each other and work very hard together as a team, so that's how we got charged for that game," said Sigfridsson.
"I think we will be happy with the bronze. Of course were not satisfied we didn't get to the final but we said we wouldn't cry if we came home with a medal so that's what we have to live with."