Judy Murray’s team had already seen their hopes of promotion to World Group II dashed by defeat by Romania in the group stage.
Tara Moore beat Tamira Paszek 6-2 6-4, while Heather Watson overcame world No38 Yvonne Meusburger 6-4 6-2 to claim her fourth singles win of the week.
Great Britain’s ranking will slip from 17th after failing to match the past two years, when Britain have made it through to the World Group II play-offs.
Team GB were competing without the services of British No1 Laura Robson due to a wrist injury.
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