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The 32-year-old won gold at the Beijing Games in 2008, and silver at London four years later.
However, she came fifth in her semi-final on Sunday, and afterwards told BBC Sport she is "getting old".
"I think it's one minute to midnight and this girl is about to turn into a pumpkin," she said.
"I think it's coming to an end, training is getting harder.
"I have been stuck in one gear all season. I am disappointed but I am happy I made it this far. These girls are fit and I wasn't able to compete with them."
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Compatriot Emily Diamond also failed to make the final, finishing sixth in the second semi-final.
In the 1500m, Scot Laura Muir matched 2015 world champion Genzebe Dibaba to qualify for the final, finishing third in the second semi-final.
Laura Weightman took the fifth qualifying spot from the first semi-final, but suffered a gash on her right shin which she said afterwards may need stitches.
And in the high jump, London 2012 bronze medallist Robbie Grabarz qualified for Tuesday's final, but team-mate Chris Baker missed out.
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Great Britain's Christine Ohuruogu hinted she will retire from athletics after failing to qualify for the 400m final at the Rio Olympics.