Great Britain Davis Cup captain Leon Smith said he was "extremely proud" of his team after the 3-2 semi-final defeat by Argentina in Glasgow.
Britain hit back from 2-0 down to force a decider, but Leonardo Mayer beat Dan Evans 4-6 6-3 6-2 6-4 to seal victory.
It ended a seven-tie winning run that included last year's final - Britain's first Davis Cup triumph for 79 years.
"We've had an unbelievable run in this competition over the last couple of years," Smith told BBC Radio 5 live.
"I don't think people would have mapped that out a few years ago, what the team has achieved, so I'm extremely proud of them."
It was only the third defeat in 17 ties stretching back to 2010, when Smith took charge for a lowly Group 2 Europe/Africa relegation play-off against Turkey.
Andy Murray won 11 points as he led the side to the title in 2015, but Britain achieved their first World Group win without him when they beat Serbia in July.
With Kyle Edmund, now ranked 55, and Evans, who is at a career-high 53, Smith is less reliant on the combination of Murray and a strong doubles team.
"That's a big plus," said Smith. "I've been saying for a while the most important thing is what the players are doing on a week-by-week basis.
"To have singles players in the draws at ATP 500s, Masters Series, main draw of Grand Slams... it's much, much better. So when we do get together for Davis Cup we now have better depth. Long may that continue."
Murray, the world number two, will remain the lynchpin for any immediate hopes of another Davis Cup success but says he is in need of a break.
The 29-year-old, who has enjoyed a hugely successful summer that included victories at Wimbledon and the Olympic Games, felt the effects of a gruelling season in the latter stages of Sunday's win over Guido Pella.
"I've never really had any muscle injuries before," said Murray. "That was worrying for me and thankfully I managed to get it done in straight sets. I was still moving okay, but when you get pain in your body it distracts you."
Murray is scheduled to return in Beijing next month, while Britain will learn their 2017 first-round opponents at the Davis Cup draw on Wednesday.
Russell Fuller, BBC tennis correspondent:
"Britain's hopes of winning back to back titles for the first time since the 1930s were ended by the better team.
"Three different players won singles points for Argentina, with only the Murray brothers contributing for Britain. That was ultimately the difference."