The government motion to extend Article 50 beyond the official Brexit deadline day, seeks a delay until June 30, on the condition MPs back May's negotiated deal by March 20.
She said parliament faced "unenviable choices" if it voted for an extension, including revoking Brexit, holding a second referendum or leaving with another deal.
The US and the United Kingdom struck a deal in February to replicate current EU-made trade deals post-Brexit.
The House of Commons voted 391-242 against the divorce deal, even after May secured further guarantees from Brussels over its most controversial elements.
Jeremy Corbyn, leader of the main opposition Labour party who has been trying to force snap elections, said May must now admit that her government's overarching strategy had failed.
An amendment to hold indicative votes on the next steps in the Brexit process, which would have given MPs the opportunity to take control of Brexit, was also defeated by a mere two votes. The latter scenario - dubbed a "no-deal Brexit" - would, according to most experts and critics, be an unprecedented act of economic self-harm.
If no deal was agreed by March 20, "then it is highly likely the European Council at its meeting the following day would require a clear objective for any extension, not least to determine its length, and any extension beyond 30 June 2019 would require the United Kingdom to hold European Parliament elections in May 2019", the motion said.
Hilary Benn told the Press Association: "What we've won today - although we lost the vote on my amendment - is Stephen Barclay confirmed that the Government will bring this so-called neutral motion back by the 25th and we will have a chance to amend it".
Any delay in the Brexit process would require the unanimous approval of all 27 remaining European Union member states, which in effects gives the bloc the power to dictate the terms of an extension.
The government lost the vote by 321 votes to 278, forcing Mrs May to give MPs a vote on delaying Brexit tonight.
It follows a night of drama in Parliament, with MPs voting to take a no-deal Brexit off the table in any circumstances. Britain will need to show how it could use more time to find a way forward, when it has so little to show for two-plus years of political infighting.
Ahead of the votes, the Independent Group of MPs are pushing ahead with a cross-party amendment calling for a new Brexit referendum despite expecting it to be voted down, sources said.
But a longer deadline still wouldn't offer a guarantee that the British Parliament would agree a deal in that time - it might just prolong the arguments.
Lawmakers have twice thrown out the Brexit withdrawal agreement May agreed upon with the bloc.
"It's still really hard to see how the numbers stack up for Theresa May, but she's giving it one more go", he said.
However, she was torpedoed by legal advice from her Attorney General Geoffrey Cox, who said the changes would not allow Britain to leave the backstop of its own accord, raising fears that the country would be stuck in an indefinite customs union with the EU.