Edmund, drafted into the singles line-up after the withdrawal of Murray with an elbow injury, was made to pay for letting slip a 5/2 lead in the second-set tiebreak.
"I was especially happy with my serve".
Like Spain, 2015 winners Britain did not win a set in Rouen.
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 24-year-old La Marsa-native upset former top-10er and current world No56 Marcos Baghdatis (who just last year was a runner-up at the ATP 500 Dubai tournament) 7-5, 7-6 (2), 4-6, 4-6, 6-1 in the second rubber of the tie to give the Tunisians a 2-0 lead. Playing for our country in the official team competition - the only official team competition we have in [this] sport - is definitely very special for me personally and for all of us as a team.
"I'm still very emotional out there".
World number 19 Pablo Carreno-Busta will instead lead Spain's assault on a first semi-final spot since 2012.
Spurs fans revel in Vincent Janssen's game-changing display against Swansea
Mauricio Pochettino has hailed Tottenham's "big character" and says it has been crucial in the club contesting for titles again. Despite the defeat Palace have been in vast form, having won their last four games in a row before Southampton .
"They are motivated because for a long time they have not won the title and I believe that they still remember the Belgrade defeat".
"There is no greater honour", Thompson said after the match.
Serbia's Novak Djokovic celebrates after winning a point against Spain's Albert Ramos-Vinolas during their Davis Cup quarterfinal tennis match, in Belgrade, Serbia, Friday, April 7, 2017. The crowd was unbelievable.
Steve Darcis rallied to beat Paolo Lorenzi 6-7 (3), 6-1, 6-1, 7-6 (4) for his 21st win in Davis Cup singles.
That left world number 14 Goffin to double down and he beat Seppi 6-4 6-3 6-3. "It also helps when you play at home on this fast surface with overwhelming fan support. I am really looking forward to tomorrow and hopefully we will finish with a victory at the end of the weekend". It was a really nice atmosphere - the stadium is unbelievable.
"They've got a great team", Kyrgios, who lost a thrilling Miami semi-final against Federer last week, told the Davis Cup website.
Pouille gave hosts France a winning start in the quarter-final with a 7-5, 7-6 (8/6), 6-3 victory over Kyle Edmund.