Canada needed to be perfect after dropping the opening two singles matches of the best-of-five series on Saturday, and Ottawa's Gabriela Dabrowski got off to a promising start by taking a 4-1 lead in the first set against Karolina Pliskova.
Canada's faint hope quickly evaporated. Pliskova, world's 22nd-ranked player stormed back to win the match 6-4, 6-2 and send the Czechs to a semifinal meeting with France.
"After (Pliskova) won the first set, she settled down and was more relaxed," Dabrowski said. "But I gave my best on every point regardless of whether I was up 4-1 or I lost the first set or I was down in the second. I was trying my hardest the whole time."
With the tie already won, the Czechs completed the sweep when Denisa Allertova and Lucie Hradecka defeated Dabrowski and Montreal's Francoise Abanda 6-1, 7-6 (2).
"It wasn't the result we were hoping for," said Canadian team captain Sylvain Bruneau. "I knew it would be difficult to win this but I thought we had a chance. I told them to give it their all and take advantage of the opportunity. I felt they really tried but the level as of now is just not as high as the Czechs."
Canada, who was competing in the eight-team World Group for the first time, will now be forced to participate in a World Group play-off on April 18 and 19 to try and keep its place in the highest level of Fed Cup play for 2016.
A win would maintain Canada's position in the World Group while a loss would drop the squad back down to World Group II. The official draw for the World Group playoffs will take place on Tuesday.
"April will not be an easy tie," Bruneau said. "Whoever we play it will be a tough country. Hopefully we have some of the players we were missing this weekend to help us but the experience that our girls had this weekend could also serve them well in the future."
The weekend matchup was missing several key players. Eugenie Bouchard, ranked seventh in the world, declined to play for Canada.
The Czechs were missing world No. 4 Petra Kvitova and No. 15 Lucie Safarova.