World welterweight champion Demetrius Andrade sealed the US team's worst Olympic boxing performance when he lost 11-9 to South Korea's Kim Jungjoo.
The only American fighter to reach the semis is heavyweight Deontay Wilder, who struggled to beat Morocco's Mohammed Arjaoui on countback.
The US have won a record 48 Olympic boxing golds and had previously never left Games with fewer than two medals.
Andrade became the latest boxer to complain about the judges' scoring.
"I fought my heart out but sometimes life is unfair," he said. "I was landing a lot of punches but the judges were not giving them to me.
"It's tough for the kids back home who want to take up boxing because if they come to the Olympics to be treated like this, there's no point in coming at all."
Wilder, who will take at least bronze, nearly followed Andrade out, escaping defeat only after being awarded two points in the final round when Arjaoui was warned for keeping his head low.
Manus Boonjumnong had earlier kept alive his hopes of becoming the first Thai to win successive Olympic boxing titles when he outpointed world light-welterweight champion Serik Sapiyev of Kazakhstan.
The 28-year-old, who will turn professional after the Games, proved smarter and more accurate than Sapiyev to win a 7-5 decision and make sure of at least bronze.
"It was really tough," Manus said. "He was aggressive, always moving forward to attack. I was anxious."
Manus will next meet Rosniel Iglesias, who provided further evidence Cuba have lost none of their might when he outpointed Russian world championship silver medallist Gennady Kovalev 5-2.
The only country to have qualified a boxer in all 11 weight classes, the Russians have not fared that much better than the Americans and are down to three men.
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