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The 33-year-old Scot twice suffered two-second penalties as she clocked a disappointing time of 105.70 seconds.
Spain's world number two Maialen Chourraut won gold (98.65), improving on her bronze at London 2012.
New Zealand's Luuka Jones took silver (101.82), ahead of Australia's Jessica Fox - the pre-event favourite.
Olympic 2012 silver medallist Fox finished with a time of 102.49 seconds after incurring a two-second penalty on gate 22.
GB won their second canoe slalom medal in Brazil earlier on Thursday, David Florence and Richard Hounslow claiming silver in the C2 double.
Team-mate Joe Clarke won gold in the kayak K1 on Wednesday.
Helen Reeves, Olympic bronze medallist and BBC Sport analyst:
"It was a tough ask for Fiona Pennie in the final, but she has improved from the Olympics in 2008 when she failed to get past the heats.
"She will be disappointed because she knows she is capable of more.
"She was in quite a good position going into bottom half, but she ran out of steam."
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Fiona Pennie could not win a third British medal in the Olympic canoe slalom after finishing sixth in the women's kayak single final at Rio 2016.