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The Belarusian won the opening three games before Drinkhall, who saved eight match points, won the fourth 17-15.
He threatened a remarkable comeback with a 11-7 win in the fifth game, but Samsonov won 11-8 in the sixth.
"I let it slip a little bit but I didn't do that much wrong," Drinkhall said.
Drinkhall, 26, became only the third Briton to make the last 16 when he beat Croatia's Andrej Gacina on Monday.
"I believe in myself, I want to win and after winning the fourth set I really found my timing and felt on top of my game," he added.
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Britain's Paul Drinkhall narrowly missed out on reaching the Olympic table tennis quarter-finals, beaten 4-2 by Belarusian Vladimir Samsonov.