The U.S. were beaten 3-2 as Williams and Alison Riske were thrashed 6-0 6-3 in the doubles rubber by Errani and Flavia Pennetta, meaning they were relegated to World Group II.
"Today has been a big eye opener," Williams said afterwards. "I'm totally not as ready for the claycourt season as I thought I was. Now I'm in the mindset of, 'You know what, I'm not on hard court.' I'm playing like I'm on hard court and I'm not.
"So I have to play and be ready to hit a thousand shots if necessary."
Williams, 33, won her 19th singles grand slam at the Australian Open and her dominance has raised talk of her claiming all the majors this year.
The French has been her least successful of the four though despite claiming the title in Paris in 2002 and 2013.
Her doubles defeat on Sunday blotted an otherwise flawless Fed Cup record and left the U.S. facing a battle to get back amongst the elite nations next year.
"We have to work harder," U.S. captain Mary Joe Fernandez said. "We came close today and need to just keep plugging away.
"The good news is that we have a lot of players in the top 100 and, hopefully, we can get two wins next year and get back into the World Group."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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