Johanna Konta was thrashed 6-0 6-1 by Olga Govortsova and Heather Watson fared little better as she was defeated 6-4 6-1 by former world No 1 Victoria Azarenka.
Konta was never allowed to get into a rhythm by Govortsova, who has slumped to 156th in the world rankings, 11 places below her British opponent.
But she showed more of the form that took her to No 35 in the world six years ago and cruised to victory in a game Britain had targeted as vital, given the tough task Watson was facing.
Azarenka broke the British No 1 early, but Watson stuck to her task and broke back, only to drop her serve and allow the dual Australian Open champion to take the opening set.
And the second proved more of a one-sided affair, meaning Britain will be back in Europe/Africa Zone Group 1 action again next year.