Marino, from Vancouver, dropped a 6-3, 6-0 decision to Karolina Muchova in the first rubber. Marketa Vondrousova followed with a 6-4, 6-1 victory over Leylah Annie Fernandez of Laval, Que.
Marino, who made a comeback to the sport last year, was making her first Fed Cup appearance since 2011.
“For sure it is disappointing to lose the match, but to have been able to get here in the first place, I am very proud of myself,” she said. “It was a good match. I started out a bit nervous, but was able to settle into the match halfway through the first set.
“There were a lot of good points, unfortunately some of the key ones did not go my way today.”
It was the Fed Cup debut for the 16-year-old Fernandez.
“My main goal is to go out onto the court and play some good tennis for the fans and for my team,” she said. “I went out and fought for every point and gave it everything I had. I feel like I am able to compete with these types of players on tour and I am taking a lot from this first Fed Cup match.”
Reverse singles and the doubles match were scheduled for Sunday in the best-of-five tie. The top-ranked Czech Republic is a heavy favourite to beat 11th-ranked Canada.
Ottawa’s Gabriela Dabrowski and Toronto’s Sharon Fichman were tabbed to play Barbora Krejcikova and Marie Bouzkova in the fifth rubber.
The winning team will advance to the World Group while the losing team will fall to the World Group II level for 2020.