Speaking at a summit in Brussels, she said there was still "work to do" but there had been progress and talks over "further clarification" would continue.
Pro EU protesters demonstrate outside the British Houses of Parliament in central London, Dec. 11, 2018 after British Prime Minister Theresa May's decision to postpone the Brexit deal Meaningful Vote.
But despite her victory Mrs May faced calls from opponents, led by Jacob Rees-Mogg, to resign.
The result of the Conservative MPs votes was 200-117.
But her allies claimed her 200 votes she won were one more than the 199 when she secured the Tory leadership in 2016 and were relieved that she can not be challenged again for another 12 months.
Mrs May said she was "crystal clear" to European Union leaders about the need for assurances on the backstop and welcomed commitments by other European Union leaders to try to get a new trade deal in place "speedily" so that the backstop would not be needed.
"Following this ballot, we now need to get on with the job of delivering Brexit for the British people and building a better future for this country".
This would be a huge mistake: it was Labour's firm stand, its refusal to back May, and its taming of rebels that forced May into this weakened situation.
"That must start here in Westminster, with politicians on all sides coming together and acting in the national interest".
"As Europe we reaffirmed our commitment to the need for a backstop, and not just because it protects Ireland and ensures no hard border between Northern Ireland and Ireland, thus protecting the peace process and the Good Friday Agreement, but also because it's a European issue too, and an open border between Northern Ireland and Ireland can't become a back door into the single market".
Reacting to his defeat, Mr Rees-Mogg said Mrs May should resign "as soon as the Queen has a moment in her diary to see her".
He said: 'The real reason we should have another referendum is that we have had 30 months of negotiation and let's be clear, we are in crisis mode on this'.
While May's position as party leader - and prime minister, as long as there is no snap election - is safe for another year, her struggle is far from over.
Nadine Dorries said: "The PM has secured the confidence of the parliamentary party tonight".
'The clock which should never have been set ticking now ticking ever louder as we approach the midnight hour.
"Votes against them, letters going in late, nothing matters to ERG".
In a detailed Brexit interview, James took the opportunity to bring up remarks made by Leave-supporting Tory MPs.
European officials said no further EU summits are scheduled before January 21 - by which time May has said the deal will have gone to parliament - and the British leader has not requested one. "But I have also heard loud and clear the concerns of those who didn't feel able to support me", May said.
She warned her European Union counterparts that failure could mean Britain crashing out of the bloc without a deal, "with all the disruption that would bring".
He added: "We don't want the United Kingdom to think there can be any form of renegotiation, that is crystal clear".
Discussing the guarantees offered, Mr Rutte said: "She will now clearly study that outcome she might have questions about it".