The race – which also started at Trocadero before heading out of the city towards the Chevreuse Valley – got off to a muted start, with Burkina Faso’s Awa Bamogo and then Slovakia’s Nora Jencusova the early movers at the front.
Jencusova built a healthy lead of more than three minutes, but chasers were on her tail around the 100km-to-go mark.
The race continued to prove unpredictable but in the first key moment, with about 50km remaining, the bunch was split in a crash that downed American Chloe Dygert, with all three Britons part of the group that broke away.
On the three laps of the cobbled Butte Montmartre climb, the British trio all made attacks of their own, but were quickly reeled back in.
British champion Georgi was best placed with 10km left, part of the group chasing down Vos and Vas, but slipped behind on the final climb.
“I’m actually a bit gutted. I felt really good all day and I was hoping something special could happen, but my legs just said no and I couldn’t follow,” she told BBC Sport.
“Fifth is nice, but in that situation, you start thinking ‘what if?'”
Henderson, who won time trial silver last Saturday, said: “I wish I could have done more for Pfeiffer, I had one speed today.
“I think I was still stuck in last week.”
Faulkner was a late addition to the US road race team, replacing Taylor Knibb who chose to focus on the time trial and triathlon. She finished both in 19th.
Faulkner will also race on the track at these Olympics, competing in the team pursuit for which qualifying starts on Tuesday.
Belgium’s Remco Evenepoel won the men’s road race on Saturday, adding to his time trial gold won on the first day of the Games.
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