The doubles was much tighter and Murray and Inglot had chances to win each of the first three sets but instead suffered a narrow 7-6 (9/7) 5-7 7-5 7-5 defeat to end their campaign for another year.
Great Britain's defence of the Davis Cup ended at the quarter-final stage after losing a third consecutive rubber to France on Saturday.
France will play Serbia in the semi-finals, after they took an unbeatable 3-0 lead over Spain in Belgrade yesterday. "Not part of the tie proper but if it is a dead rubber a junior gets to play, I think that's a good move, or an under-21 player or something like that, legends event, - there's different ways to do it, but yeah today was a great atmosphere but this nation's quite unique in their love for tennis that way".
Having won a 12th successive singles rubber in the tournament on Friday to set Serbia on their way to this weekend's quarter-final victory against Spain, the 12-time major victor is crucial to his country's hopes of returning to the final for the first time since 2013.
The rubber had lacked a serious air before the fun began, with Benneteau selected ahead of France's best player, Lucas Pouille. I don't need Davis Cup players.
Edmund, ranked 47th, was filling in for top-ranked Andy Murray, who's nursing an elbow injury.
After straight-sets defeats for Kyle Edmund and Dan Evans on day one at Rouen's Kindarena, the chances of an away win were remote at best. They have not met since the 2010 final, which Serbia won 3-2 at home. It's just hard. Sort of different tennis.
That stat in itself is a measure of the improvement that has been made by the British team on the Davis Cup circuit in recent years, culminating with the title in 2015.
"I enjoyed it. It was always going to be that way, I guess".
He had not played a match of any sort on the red stuff since the summer of 2014 and has made no secret of his dislike for it.
In Belgrade, world number two Novak Djokovic helped Serbia to victory in their last-eight tie against Spain.
But there can surely be no greater opportunity for them to make their point about the drama and spotlight the competition offers than in Saturday's contest against the formidable partnership of Julien Bennetteau and Nicolas Mahut.
Andreas Seppi and Simone Bolelli beat Ruben Bemelmans and Joris de Loore 4-6 6-3 6-4 3-6 7-6.
Elsewhere Italy kept their semi-final hopes alive with victory in the doubles over Belgium in Charleroi.
But, if that was unlikely, this was miracle territory - winning the doubles a formidable task even before considering Sunday's reverse singles.
And in 2017, the Briton came up just short of beating No3 Stan Wawrinka in Brisbane's quarter-finals, and did the same against Milos Raonic in the quarters in Delray Beach.