His elimination cuts Great Britain's boxing entry to just one, the heavyweight Fola Okesola, who fights the American Nate Jones on Thursday.
Burke, 21, left himself with too much to do going into the last round. He was 10-6 behind and did everything he could to narrow the margin, but Huste stretched his advantage to 12-6 half-way through the final session.
Burke rallied to make it 12-8 with a mid-ring attack but was undone by the four-point margin.
Ireland's Brian Magee came off the canvas to beat Randell Thompson, of Canada, in the first round of the middleweight tournament.Reuse content