Huston, who was 38th in qualifying, had earlier progressed from the last 32 by beating Dutchman Rick Van Der Ven with his final arrow.
However, his Olympic Games debut was later ended as Bonchan won 6-0.
There was Just two points between the pair in the first two sets, and one point in the third.
Huston was the first British athlete in Olympic Games action in Rio last Friday.
The archer was competing minus his trademark flat cap after it fell foul of the British Olympic Association's dress code.
Belfast man Patrick Huston was beaten by Korea's Ku Bonchan at the last-16 stage in the men's individual archery at the Olympic Games on Wednesday.