Nick Kyrgios surprisingly did not play for Australia, being left with a cheering role because of a collarbone injury picked up on Wednesday.
Troicki, who helped Serbia win the Davis Cup in 2010, said: "I probably feel the worst ever".
"That's just the way the cards fell".
It was a disappointing way to go out of the Davis Cup for Australia after their impressive wins over Belgium and Colombia in the group stages.
The ATP and the ITF, who run world tennis, have been involved in a bitter stand-off for years over the Davis Cup, which is now being played in Madrid, and the announcement of the former's new-look event last year by Gerard Pique's Kosmos Group only strengthened the feud.
'I think they should have played the tie'. "We were surprised", Pospisil said.
"The main thing is that everybody here did their part, you know, not just now, but during their career", he said. The Americans spoke as if they still had a chance to advance after beating Italy on Thursday, but the team had already been eliminated.
The victory would come shortly before 2 a.m. when veteran duo Feliciano Lopez and Marcel Granollers beat Khachanov and Andrey Rublev 6-4 7-6 to clinch a 2-1 win.
Shapovalov and De Miñaur had previously met in the 2015 junior Davis Cup final and in the 2016 Wimbledon boys final.
The remarkable rise of Canadian tennis continued as Denis Shapovalov and Vasek Pospisil combined to defeat Australia and become the first semi-finalists of the new-look Davis Cup. It's a lot of responsibility and pressure on them because this is the most traditional, historic team event in our sport, over 100 years.
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"So we're coming into the quarters now and playing against Russian Federation tomorrow".
"So a few of the guys apologised to me".
Andy Murray was among the players who complained of a format flaw that allowed Canada to forfeit its doubles against the USA on Tuesday, handing the Americans a 6-0, 6-0 victory that could have affected other teams trying to qualify for the quarter-finals.
The victor of Thursday's series between Serbia and top-ranked France will guarantee a spot in the quarterfinals.
Filip Krajinovic had defeated Yuichi Sugita 6-2, 6-4 in the first match.
But Millman eventually lost to world no. 150 Pospisil in straight sets, 7-6 6-4.
While there have been plenty of teething problems for the inaugural version of the revamped Davis Cup, the knockout phase looks enticing as world number one Rafael Nadal bids to lead Spain to the title on home soil.
Germany only needed to win one rubber against Chile to guarantee finishing top of their group and secured that at the first opportunity when Philipp Kohlschreiber beat Nicolas Jarry 6-4 6-3.
That put the Canadians through to the quarter-finals but, with the two best-placed runners-up across the six groups progressing to the last eight, the 6-0 6-0 scoreline awarded to the USA could help them in comparison to other teams. Argentina survived as one of the two best runners-up.