David Davies said the MPs should not be in government.
Wales' First Minister Mark Drakeford welcomed the vote as a "step in the right direction".
Immediately after the defeat, the Prime Minister confirmed that MPs will today be vote on whether the Government should ask the European Union for Brexit to be delayed beyond the March 29 scheduled departure date.
This was amended against the government's wishes to be stronger - opposing no-deal in all circumstances.
MPs will vote on whether Parliament wants to seek an extension to Article 50 - delaying the UK's departure beyond the current March 29 deadline - on Thursday.
But, in a dramatic turn of events MPs has earlier gone against the Government on an amendment to the motion which called to rule out a no deal completely.
On Thursday, MPs will be asked if they want to delay Brexit until 30 June to allow legislation to pass parliament, but that is only if MPs back Mrs May's deal by 20 March.
She hinted she will hold a third "meaningful vote" on the Brexit deal next week in a last-ditch bid to convince Tory rebels they must back her or risk Brexit never happening. I told her it was a disgrace.
A minister resigned and four Cabinet members abstained from voting after the Government changed its mind last minute and voted against its own motion.
"They should resign, or be sacked".
European Commission president Jean-Claude Juncker said that Brexit should be completed before the European elections which take place between May 23 and 26.
A Downing Street source said ministers who voted against the Government would be expected to resign.
However, it was reported last night that ministers had been told it was OK to abstain.
Simon Hart, Tory MP for Preseli Pembrokeshire, said he was not "entirely surprised" by Wednesday's vote.
"I am concerned that the vote was so narrow and so that many MPs are prepared to support a no deal Brexit".
"It's Theresa May versus the world".
How long would the extension to Article 50 be?
Glyn Davies, Tory MP for Montgomeryshire, said: "The government is going to have to accept that parliament is going to have a say, and that's a pretty big step I think".
The pound to euro and dollar exchange rates leapt overnight - soaring past Wednesday morning's highs after Theresa May's Brexit deal was rejected.
"That includes 10 DUP MPs who clearly had their fingers in their ears today as our business community detailed the devastating consequences of a no deal Brexit".
Guto Bebb voted for it, while Stephen Crabb abstained.
"It's clear that the House of Commons has to find a consensus around something and if it isn't the prime minister's deal I think it is likely to be something which is much less to the taste of those on the hard Brexit wing of my party". Unless MPs decide to back the Prime Minister's deal, or back an extension to Article 50, the default option is still a No Deal Brexit.
"This does not need to be a long extension".
Chamber of Commerce and Industry chief executive Ann McGregor said: "NI Chamber welcomes the result of the vote".
Andrew Bridgen, a eurosceptic lawmaker from May's Conservative Party accused her of pursuing a "scorched earth" policy of destroying all other Brexit options to leave lawmakers with a choice between her deal and a delay of a year or more.
FILE PHOTO: Britain's Prime Minister Theresa May speaks in Parliament following the vote on Brexit in London, Britain, March 13, 2019.
Calling for a further referendum, she added: "The only way forward now is to seek a compromise position across the House and put that back to the people".