The world champion, who faced being banned for the Games after missing three drugs tests, finished fifth.
Dutch rider Annemiek van Vleuten went to hospital with severe concussion and three small fractures in her lower back after crashing as she led the race.
Team-mate Anna van der Breggen won gold, ahead of Sweden's Emma Johansson and Italy's Elisa Longo Borghini.
Van Vleuten later tweeted to say she was "fine" but "super disappointed after best race of my career".
Watch: Follow the winding descent of the women's road race
London 2012 silver medallist Armitstead, 27, was cleared to compete at Rio after a successful appeal and was in contention until the final stages.
Van der Breggen won the 141km race in a time of three hours 51 minutes 27 seconds, ahead of Johansson and Longo Borghini, who took bronze.
However, the race was marred by Van Vleuten's crash.
The 33-year-old had sped off from the pack when she came off her bike on the descent of the steep Vista Chinesa, where several men - including Britain's Geraint Thomas - crashed on Saturday.
Van Vleuten was taken to hospital where Dutch cycling officials later said she would spend the next 24 hours in intensive care.
British former Olympic champion Chris Boardman, working as an expert analyst for BBC Sport, believes the Rio course was "too dangerous".
"I'm actually quite angry because I looked at the road furniture and thought nobody can crash here and get up," he said.
"This was way past technical, this was dangerous."
Cycling's governing body, the UCI, defended the course, saying it "was carefully designed and extensively tested.
It added: "We do our utmost to design safe, challenging courses but unfortunately crashes do sometimes occur due to a combination of factors."
Van der Breggen, 26, said Van Vleuten's crash made her more determined to win gold for the Dutch.
She won the sprint to the line along the Copacabana, holding off Johansson and Longo Borghini as the trio overtook American Mara Abbott on the straight.
"I was pretty shocked about it, I think she crashed hard," said Van der Breggen. "I realised I was first in the team and had to chase. We knew we had to do it."
Armitstead, the world and Commonwealth champion, was one of the pre-race favourites.
But the Yorkshire rider's preparations were hampered by the possibility of a ban for missing three drugs tests - and the increased scrutiny she faced when the news emerged.
She avoided a suspension of up to two years by winning a Court of Arbitration for Sport (Cas) appeal.
Not only did Armitstead face questions about her mental focus as she lined up, many wondered whether she had the physical capability to cope with the mountainous course in Rio.
She responded with a gutsy performance on a course she described as "brutal", but ultimately missing out on a second Olympic medal.
Armitstead was part of a group that wiped out a gap of over a minute between themselves and the breakaway as they climbed Vista Chinesa.
"I felt a little bit like a zombie going into it - not much sleep in the past few weeks," she said. "But when I'm on my bike I'm doing what I know and what I am in control of and my brain soon switches once I have got a number on.
"There are no excuses. I simply wasn't able to climb fast enough."
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Britain's Lizzie Armitstead missed out on an Olympic medal in a women's road race marred by a horrific crash.