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In a close fight, in which two of the three judges scored it in favour of Argilagos, 23-year-old Yafai was narrowly edged out.
Richie Woodhall, who won Olympic bronze in 1988, said he was "proud" of Yafai.
"The fight warranted either a semi or a final," he said. "They are two of the best in the world at this weight."
Elsewhere in the men's light-flyweight, Ireland's Paddy Barnes - bronze medallist in 2008 and 2012 - suffered a surprise elimination at the hands of Samuel Carmona Heredia by points decision.
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Great Britain's Galal Yafai was beaten by Cuba's world champion Joahnys Argilagos in the last 16 of the men's light-flyweight competition.