Denmark were already handicapped going into the tie with neither Clara Tauson nor Caroline Wozniacki at their disposal and Johanne Svendsen and Rebecca Munk Mortensen were not able to pull off a surprise in their singles' matches against Rebecca Sramkova og Viktoria Hruncakova.
First single, Johanne Svendsen, number 697 in the world ranking, put on a brave performance but lost 6-7, 7-5, 3-6 to Sramkova, who is number 37 in the world rankings.
In the second match, Munk Mortensen lost 4-6, 3-6 to Hruncakova, who ranks more than 500 places above the Dane in the world.
A Billie Jean King Cup match consists of three individual matches, two singles and one doubles, so the two Slovak singles victories were enough to seal the overall win.
In addition to Slovakia and Denmark, USA is the last team in the group.
The Danish tennis women will face USA on Saturday and must win the match to preserve their hope of a place among the world's eight best nations, who meet each other at the Billie Jean Cup Finals at the end of the year.
Only the winner of the group advances to the finals.