Dynamo Kiev midfielder Gerson Rodrigues condemned the Irish to their second defeat in as many Group A games with a superb long-range effort five minutes from the end.
“It was a horrible and embarrassing night,” Ireland skipper Seamus Coleman told the BBC.
“We got what we deserved which was nothing. I don’t think we demanded the ball enough and looked to break them down as quickly as we could.”
Ireland sit bottom of the group on zero points, four behind leaders Serbia and Portugal who drew 2-2 in Belgrade.
Luxembourg meanwhile are a point behind the two leading teams after a rare World Cup qualifying victory for the Red Lions.
The win at the Aviva Stadium came thanks to smart play from the 25-year-old Rodrigues, who pounced on a knockdown to lash home his sixth international goal.
Luxembourg have never qualified for a major tournament and have little chance of making it out of the five-team Group G and to next year’s finals in Qatar.
However, Luc Holtz’s side inflicted an humiliating defeat on Ireland.
Stephen Kenny is still looking for his first win as Ireland boss, with his run of games without a win since taking charge last year now at 10.
His next opportunity will come on Tuesday when Ireland face World Cup hosts Qatar in a friendly in the Hungarian city of Debrecen.
