Milos Raonic, the world number 13, sealed Canada's first passage to the quarter-finals with victory against 82nd-ranked Guillermo Garcia-Lopez, drafted into the Spain side in the absence of Rafa Nadal, David Ferrer and Nicolas Almagro.
Nadal is returning from seven months out with a knee injury in Chile this week, while Ferrer and Almagro were unavailable after gruelling runs to the last four and last eight of last month's Australian Open respectively.
Spain captain Alex Corretja, in his second campaign in charge after inheriting a team that had won the cup three times in five years and were losing finalists last year, said he respected players' desire to recuperate rather than add to their packed calendars.
"Players are on their own to decide if they want to play or want to rest," Corretja told the Davis Cup website.
"It's not like we were underestimating Canada; not at all," he added.
"Our players didn't come because their calendars are very busy and they chose another option but we have no regrets about the ones who didn't come or the ones who were here.
"They were trying to do their best and for us it's always a big disappointment to go out in the first round."
Spain's defeat on the indoor hard court in Vancouver means they will have to wait until April's draw to discover their opponents for September's play-off.
It is the first time they have lost in the first round since a defeat to Belarus in Minsk in February 2006 when they were also missing Nadal.
They went on to beat Italy in the play-off to restore their world group status and lost to the United States in the quarter-finals the following year.
"When we drew Canada I knew it was going to be difficult for many reasons, especially on this surface," Corretja said. "Canada did better than us and we need to congratulate them."