Emma Raducanu and Harriet Dart won and lost one match each during the Billie Jean King Cup, but with the scores locked at 2-2, Dart and partner Katie Swan suffered defeat in the doubles clash.
Raducanu earlier marked her clay debut with victory, beating Tereza Martincova on Friday before suffering a 6-1 6-1 defeat a day later to Marketa Vondrousova due to injuries and blisters.
Dart kept the tie alive with a 6-0 5-7 6-2 victory over Linda Fruhvirtova, but Great Britain weren't able to seal the victory despite their admirable effort.
In the doubles match, Dart and Swan lost 6-1 7-5 to Czech pair Marketa Vondrousova and Karolina Muchova.
Raducanu was expected to play in the doubles match, but with her blistering still causing issues, she decided to sit out.
With the tie ending 3-2 in favour of Czech Republic, they have now qualified for the 12-team finals in November, while Great Britain will now play a play-off tie in the same week to try and book their spot in the showpiece.
However, should Great Britain lose that tie, they could still make the finals should they be chosen to host the tournament.
It is likely to be at least another month until a decision around the hosts is announced, and success for the LTA would mean a bumper autumn of tennis, with Glasgow hosting a group stage of the Davis Cup in September followed by the Laver Cup at The O2.