The day after a parliamentary loss by the worst margin for a British government in modern times, the pressure is on May to show she can find a workaround with opposition political parties to take Britain out of its current relationship with the world's largest trading bloc.
The EU says it could extend the Brexit deadline if London provided a valid reason.
Sturgeon added, however, that the political complexities of delivering Brexit meant that the most credible option was now to offer a second EU referendum vote.
May "doesn't seem to have any clear idea herself of what the next steps are and (...) it didn't seem to me that she is prepared to abandon or move any of her red lines in order to open space for any new ideas," Sturgeon said, summarising a phone call with May on Tuesday night after the vote.
But asked whether her Scottish National Party (SNP) could support a Norway-style customs union arrangement, which might get broader backing in parliament, she said "I think that ship at the moment really has sailed."
"I don't see how that can be negotiated between now and March 29, but if (May) wants to open up any space for discussion the starting point has to be the extension of Article 50 (trigger clause for Brexit)," she told the BBC in London.
Nevertheless, she said, Brexit showed that longer term Scotland's best option was independence.
Sturgeon, who represents an area of Britain that voted to keep EU membership, has long argued that Britain's best option is to stay in the single market and customs union. She said that was already a compromise which had been "completely rejected" by the London government.
The SNP, which also runs the devolved Scottish government, has 35 of the 59 Scottish seats in Britain's 650-seat parliament
(Editing by Stephen Addison)