Injured world number two Rafa Nadal and number five David Ferrer were two of the absentees as Brazil's 3-1 success on clay in Sao Paulo dumped Spain into the Euro/Africa Zone Group I for the first time since 1996.
For a country with 10 players in the top 50 it was a bitter blow and further humiliation following setbacks for their football and basketball teams at their respective World Cups this year.
Moya, who took over from Alex Corretja at the end of 2013, announced his decision to step aside on his Twitter feed (@Charlymoya) on Thursday.
In an interview with El Pais, the former world number one said he had not been expecting to find it so hard to convince Spain's top players to take part in the Davis Cup and that he was leaving partly because he did not want to further disrupt the lives of his young family.
"I signed for one year instead of the two they offered me for family reasons," he told the newspaper.
"I have three small children and I was not sure if it would be easy for me to travel. I have realised that it is difficult."
Spain have dominated the Davis Cup over the past 14 years, winning five times in 2000, 2004, 2008, 2009 and 2011. They also finished as runners-up in 1965, 1967, 2003 and 2012.
They will begin their campaign to restore their World Group status away to either Russia or Denmark in July next year.
There was no immediate word from the Spanish tennis federation (RFET) on a successor to Moya, though Juan Carlos Ferrero, another former world number one, has expressed a desire to captain the team one day.
Ferrero, who retired in 2012, played in 17 Davis Cup ties, compiling an 18-6 record in singles rubbers, and helped them to their first triumph in the competition in 2000 and subsequent victories in 2004 and 2009.
(Reporting by Iain Rogers, editing by Pritha Sarkar)
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