"The government can not demonstrate the flexibility necessary for a successful deal if its hands are tied midway through that process", Davis said.
Facing the prospect of losing a vote on a crucial amendment to the government's flagship Brexit legislation - which was created to empower parliament to vote down the final deal without risking a "no-deal" exit from the bloc - ministers intervened with a concession at the 11th hour even as MPs were wrapping up debate on the controversial measure.
Following its defeat, the government's own amendment on the so-called meaningful vote will go forward to the House of Lords for debate next week - but with some changes.
Hours before the debate began, a justice minister resigned in protest at what he called its "wish to limit" the role of parliament in shaping Brexit. He said he would vote against the prime minister.
Remain-supporting Conservative MPs had threatened to defeat the government on an amendment known as the "meaningful vote" amendment, which would have given Parliament a wide-ranging veto to May's Brexit deal, or even bring about another referendum on whether Britain should leave the EU.
Some lawmakers tried to shout him down and accused the government of wanting too much power.
Caroline Flint, a remainer whose Don Valley constituency voted more than two to one to leave, defended her constituents who she said had been insulted "day in and day out by some of the comments in this place and outside are not against all migration".
But Britain - and its government - remain divided over Brexit, and European Union leaders are frustrated with what they see as a lack of firm proposals from the U.K about future relations. The government earlier had said it would not support that amendment.
They also voted against remaining in the European Economic Area (EEA), which offers tariff-free access to the EU's single market in return for accepting free movement of people, goods, services and capital, by 327 to 126.
"We are asking members of parliament to abide by the referendum result, our manifesto commitment and to back our country", Andrew Bridgen, Conservative lawmaker and Brexit campaigner, told Reuters.
As the vote approached, Tory MPs intending to defy the party whip in order to vote with Labour on the amendment left the chamber.
The formal separation is to happen in March 2019.
Elsewhere in a day of drama, the main opposition Labour party suffered a large rebellion by its MPs seeking to keep Britain in the EU's single market.
It has been clear for a while that the now ex-minister, one of the rising generation in the Tory party, has been frustrated for some time. She now relies on the support of a small Northern Irish party.
British Prime Minister Theresa May avoided a major blow to her Brexit strategy on Tuesday after lawmakers rejected a plan that would have given parliament a veto on the final deal negotiated with Brussels.
But rebelling on the bill for the first time, Hilary Benn, the former shadow foreign secretary, who chairs the Commons cross-party Brexit committee, said there comes a point where "we have to stand up and be counted".