She has said she would only bring it back for a third Commons vote if there was "sufficient support" for it.
Marchers set off in central London with banners proclaiming "the best deal is no Brexit" and "we demand a People's Vote" in what organisers said was more than one million people strong and the biggest anti-Brexit protest yet.
Lawmakers will now vote on a range of Brexit options on Wednesday, giving parliament a chance to indicate whether it can agree on a deal with closer ties to Brussels - and then try to push the government in that direction.
But the Brexit ministry said in a statement it was "disappointed" by the vote, adding that it "upends the balance between our democratic institutions and sets a unsafe, unpredictable precedent".
"I must confess that I am sceptical about such a process of indicative votes.No government could give a blank cheque to commit to an outcome without knowing what it is", May said, promising to "engage constructively" over the indicative votes but without any commitment on backing any particular alternative.
"When we have tried this kind of thing in the past, it has produced contradictory outcomes or no outcomes at all". Known as "indicative votes", the ballot isn't binding, but could present a way out of the impasse.
Mrs May will convene her Cabinet on Monday morning before updating the Commons on the Brexit process following last week's European Council summit, where she agreed to delay Britain's departure past March 29. Under Conservative rules, May can not face a formal leadership challenge from within her own party until December because she survived one three months ago.
If they defeat it, Britain has until April 12 to tell the European Union what it plans to do next: leave without a deal, risking economic chaos, or seek a long delay to Brexit and chart a course toward a softer exit or even remaining in the bloc.
Now a departure date of May 22 will apply if Parliament rallies behind the prime minister and she is able to pass her deal.
The government was defeated by 329 votes to 302 on the cross-party amendment, a majority of 27. Two other junior ministers resigned from the Conservative Party and supported the deal, according to unconfirmed reports.
"Meanwhile the European Commission released a comprehensive document detailing its no-deal "preparedness", stating that it is "increasingly likely" that the United Kingdom could leave the 28-member bloc without a deal on April 12". If not, it will have until April 12 to outline its plans.
May admitted yesterday she had still not secured the votes needed to get her own, twice-rejected Brexit deal through parliament, raising again the prospect that Britain could crash out of the European Union in just over two weeks' time.
British Prime Minister Theresa May arrives at church, near High Wycombe, Britain, on March 24, 2019. "If we can not, the government made a commitment that we would work across the House to find a majority on a way forward", she said.
"The view that no-deal Brexit won't happen because there is a majority in parliament against that is a bit of simplistic view".
At a meeting on Sunday at the prime minister's country retreat, Chequers, prominent Brexiteers told May they might back the deal - if she agreed to step down so that a new leader could take charge of the next phase of negotiations, which will settle Britain's future relations with the EU.
They were among 30 Conservatives who disobeyed the prime minister to support the rebel amendment.
The UK's best-selling newspaper The Sun said: "Time's Up, Theresa" on its front page and called for her to quit.
David Lidlington, effectively the deputy prime minister, is mentioned as a temporary possible successor to May, while senior party leader and former cabinet minister Iain Duncan-Smith said aides briefing against May should be dismissed for being disloyal.