Spain are through to the quarter-finals of the Davis Cup after Rafael Nadal beat Borna Gojo.
The doubles rubber was conceded by the Canadians as three of their players were declared unfit to play, an ITF spokesman said, so the final result was 2-1 to Canada, the same scoreline by which they beat Italy by Monday.
He defeated Tallon Griekspoor 6-7 (7), 6-4, 7-6 (5) on Wednesday in his first Davis Cup match with Britain since 2016.
The 20-year-old Shapovalov saved three set points before snatching the first set in a tie-break, only for Berrettini to level the match in a second-set breaker.
The British Davis Cup captain Leon Smith said there is no guarantee of Andy Murray playing singles with Dan Evans and Kyle Edmund also being in the team.
It was Canada's first win against the USA, in 16 Davis Cup ties.
Jo-Wilfried Tsonga got France off to a positive start with a straightforward 6-2, 6-1 victory over Yasutaka Uchiyama on the hard-court surface in Madrid, before Yoshihito Nishioka beat the experienced Gael Monfils 7-5, 6-2.
Canada take on the United States in their next match, with Italy facing the Americans the following day.
Britain's struggles meant the tie between Australia and Belgium to decide who will win Group D started at gone 8pm, two hours after the scheduled start time.
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The president replied, 'That was so long ago. "No one is going to know the difference, '" Howard continued. Another added, "Umm.I'm guessing Julia Roberts would very much like to be excluded from this narrative".
The Colombia doubles team of Juan-Sebastian Cabal and Robert Farah recorded a 6-7 (5), 6-4, 7-6 (3) win over Sander Gille and Joran Vliegen.
That led to controversial proposals to revamp the tournament and turn it into a season-ending 18-team event, as part of a 25-year £2.15bn plan funded by the Kosmos investment group fronted by Pique.
Barcelona footballer Gerard Pique has been at the heart of the changes after his marketing company Kosmos struck a $3billion deal over 25 years with the worldwide tennis Federation.
"I'm all for trying change if something isn't working and I'm willing to see how it goes, and excited to see how it goes", Murray told BBC Sport.
He was given a stiff workout by the 23-year-old Griekspoor, who has never played in the main draw of a grand slam and who was a surprise pick in the Dutch team ahead of Botic Van de Zandschlup.
"I think maybe the ideal format is somewhere in between".
Andy Murray and Novak Djokovic have their sights set on playing at the 2020 Tokyo Olympics. There's nothing really to complain about so far. "It's exciting, I just obviously hope each individual country gets the support that helps create the atmospheres that people expect when they turn up to Davis Cup matches".
German world number seven Alexander Zverev was clear from the outset that he would not compete and has instead made a decision to play in an exhibition match against Federer - whose management company he is signed to - in Mexico.