The 37-year-old - who will retire at the end of the current season - saw his final Commonwealth Games tournament come to a premature end following a medal-laden career in the tournament.
Matthew, who won double Commonwealth gold in Delhi before adding another gold and silver in Glasgow four years ago, lost the first set 11-7 but battled back to level things up at one set apiece with an 11-6 triumph in the second.
It was the third set which proved to be the pivotal one, though, and at 10-10 it could have gone either way before Malaysian Adnan won two points in a row to take it 12-10.
Matthew could barely have wished for a better response to that setback when he took the match to a decider with an 11-4 triumph in the fourth - taking only eight minutes to level things up.
However, the tit-for-tat nature of the match continued in the final set as Adnan won 11-6 to seal his place in the semi-finals, dealing Matthew his first Commonwealth singles defeat since 2006.