The American squad fell to 0-2 in Red Group play at Dusseldorf, Germany, following Tuesday's pair of one-sided losses.
Tomas Berdych decimated Roddick 6-1, 6-2 in a 61-minute affair in the first singles match while Radek Stepanek wrapped up the Czechs' victory with a 6-2, 6-1 rout of Blake in the second.
The dead-rubber doubles match will be played Wednesday as the Czech Republic improved to 2-0 in the round-robin tournament.
Serbia moved to 2-0 Tuesday with a Blue Group victory over Russia. In that match-up, Viktor Troicki breezed past Dmitry Tursunov 6-3, 6-2 and Janko Tipsarevic handled Alex Bogomolov Jr. 6-1, 6-3.
Florian Mayer leveled Ivan Dodig 6-1, 6-1, giving defending champion Germany a 1-0 lead in its Blue Group match against Croatia, while Argentina went up 1-0 against Japan in the Red Group when Leonardo Mayer handled Japan's Tatsuma Ito 6-4, 6-4.