Video report by ITV News Europe Editor James Mates
Theresa May has said she was "disappointed" to lose a key House of Commons vote but insisted the Government remains "on course to deliver Brexit".
Arriving at a European Council summit in Brussels, the prime minister said her flagship EU (Withdrawal) Bill was making "good progress" despite Wednesday's setback, which she said was the Government's only defeat in 36 votes on the legislation.
Tory rebels helped defeat the Government and ensure there will be a "meaningful vote" on the withdrawal deal.
EU leaders are preparing to rubber-stamp the decision to move Brexit negotiations forward to trade talks and the prime minister will hope the defeat does not damage EU leaders' confidence in her ability to lead talks.
In a night of high drama, rebel ringleader Dominic Grieve told the Government it was "too late" as ministers made last-minute concessions in an attempt to head off the revolt.
He saw his amendment to the EU (Withdrawal) Bill squeezed through the Commons by a majority of four.
It means MPs and peers will be given more control over the Government's implementation of the withdrawal agreement, as ministers will have to pass a statute, which can be amended, before it takes effect.
Speaking in the Commons on Thursday, Brexit Secretary David Davis said the vote result would lead to a "very compressed timetable" for ministers.
"The effect of it is to make the powers available under Section 9 deferred until after, as we see it, we get royal assent to the Withdrawal Agreement and Implementation Bill, which means there will be a very compressed timetable.
"Now those who want to see a smooth and orderly exit from the European Union hopefully will want to see a working statute book.
"So we will have to think about how we respond to it, but as always we take the House of Commons' view seriously and will continue to do so."
Mr Davis was responding to a question from shadow Brexit secretary Keir Starmer who asked an assurance the Government will not seek undermine or overturn the "humiliating" result.
ITV News Political Correspondent Libby Weiner believes that the Government's defeat on an amendment to the EU (Withdrawal) Bill guaranteeing a "meaningful Brexit vote" could cause Theresa May to drop plans to enshrine a Brexit date into law.
The defeat appears to have dented any political capital Mrs May gained after the European Commission said last week that "sufficient progress" has been made on divorce issues to move Brexit negotiations on to their second phase.
After a dinner with Mrs May on Thursday, the EU27 are expected to green-light phase two when they meet in her absence on the second day of their two-day summit in Brussels on Friday.
Wednesday's vote saw 11 Conservative MPs join opposition parties in backing the amendment, and a handful of others abstaining.
Mrs May sacked Tory vice chair and Brexit rebel Stephen Hammond following the vote.
The European Parliament's chief Brexit co-ordinator Guy Verhofstadt tweeted: "British Parliament takes back control. European and British Parliament together will decide on the final agreement. Interests of the citizens will prevail over narrow party politics. A good day for democracy."
Backers of a "soft" Brexit, including Tory rebels Nicky Morgan and Anna Soubry, also hailed the result.
Ms Morgan tweeted: "Tonight Parliament took control of the EU Withdrawal process".
Labour leader Jeremy Corbyn, who will be cheered by the fact that only two of his own Brexiteer MPs rebelled to back the Government, said: "This defeat is a humiliating loss of authority for the Government on the eve of the European Council meeting.
"Theresa May has resisted democratic accountability. Her refusal to listen means she will now have to accept Parliament taking back control."
Mr Grieve said he had no option but to push his amendment to a vote because the Bill gave "intransigent" ministers "the biggest Henry VIII power ever conferred on Government" with no justification.
He said his amendment would not stop Brexit but the vote provoked a furious backlash from Leavers.
Tory Nadine Dorries called for the deselection of rebel Tories for "undermining the PM", while accusing Mr Grieve of "treachery".
In dramatic scenes in the Commons, Tory rebels shouted "too late" as justice minister Dominic Raab outlined his concession and Government whips buzzed around the chamber in an attempt to win over rebel MPs.
Downing Street said it would "respect the will of MPs" but a Government spokeswoman suggested it may seek to amend the Bill during later stages of its passage through Parliament.
In a further setback, EU chief Brexit negotiator Michel Barnier has warned progress at the Brussels summit may not mean an immediate start to the trade talks which Mrs May is seeking.
Mr Barnier told MEPs the European Council would initially concentrate on the terms of a transition to the post-Brexit relationship, while he would focus on turning last Friday's deal into a legally-binding Withdrawal Agreement.
A leaked draft of a text to be considered by the EU27 leaders on Friday suggests that trade talks may not start until after a subsequent summit in March, when a further set of guidelines will be produced.