Edmondson started the points race, the last event of the omnium, in fourth place and only four points away from the silver medal.
But she plummeted out of contention and finished eighth, having scored no points in the deciding race.
It was Australia’s last chance of a medal in a disappointing track program, which has yielded only one silver and a bronze.
A few minutes after Edmondson dropped out of medal contention, compatriot Matthew Glaetzer started the consolation ride-off for seventh place in the keirin.
He had not even gone a quarter lap when he touched wheels at slow speed and fell.
That, too, was symbolic of Australian cycling in Rio, where the themes so far have been crashes and shattered dreams.
Glaetzer finished fourth after the re-start, for 10th overall.
Laura Trott dominated the omnium, finishing a whopping 24 points clear of American Sarah Hammer to win the fifth British cycling gold medal in Rio.
She is the only British woman to win four Olympic gold medals.
Earlier on Tuesday, Edmondson had won the 500m time trial and was second in the flying lap to close to within four points of Hammer and Belgium’s eventual bronze medallist Jolien D’Hoore.
But it was clear when Trott, Hammer and D’Hoore swamped Edmondson at the second intermediate sprint that the Australian was no longer a contender.
“It was exhausting – I gave it everything I could and put myself into an OK position going into the point score, but obviously I had to be aggressive instead of defensive,” Edmondson said.
“I gave it a crack.”
Asked if she ran out of legs or was marked too heavily, Edmondson said it was a combination of the two.
Edmondson said it was tough to take for Australia not to win any gold on the track.
“I think it’s just disappointment,” she said.
“As a cycling nation we’re pretty good and for us not to come home with a gold medal is pretty hard (to take).”
Edmondson was a member of the women’s team pursuit squad that finished fifth, their chances cruelled by a pre-Games training crash.
She won omnium and team pursuit gold at last year’s world titles.
German Kristina Vogel broke the British domination, beating their fastest qualifier Rebecca James for an emotional gold medal in the sprint.
This week Vogel joined the chorus of rivals wondering how the British were so good on the track at the Olympics after being “cannon fodder” in between Games.
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