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Sawyers' best jump was at 6.69 metres which meant she was the highest-ranked Briton in what was her first Olympic final.
Tianna Bartoletta of the USA won the gold, fellow American Brittney Rose earned the silver while Serbian Ivana Spanovic will take home the bronze.
"I can't believe I'm going to say it but I'm disappointed", Sawyers admitted to the BBC.
"I had two goals coming here: to make the final, and jump a PB (personal best). I made the final and I really thought I could jump my PB (6.75) in the final on the biggest stage.
"I feel like on the biggest stage I usually thrive in these enviornments and it didn't happen tonight. 6.69 is a solid performance, but it's not what I am capable of and I feel I'm better than 6.69. I am kind of gutted.
"I know I'll look back on this in a few days and be like 'you did amazing, you made an Olympic final and you made the top eight' and when I say those words out loud a smile comes to my face and I think 'that's pretty good but you always want more.
"Every time I achieve one goal I always want the next and I didn't want it to stop there.
"For that, I am gutted, but I am really proud of myself."
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