He said: "I am disappointed that Parliament has rejected the Prime Minister's renegotiated deal". It was the largest defeat for a British government in Parliament in modern times.
Simon Hart, the Carmarthen West and South Pembrokeshire Conservative MP, said: "Basically the result is that any outcome is now possible, from a deal to no deal, to a delayed deal, to the loss of the prime minister, to the loss of a government, to an election".
Labour said allowing a free vote on no-deal showed Mrs May had "given up any pretence of leading the country".
But if the deal falls, MPs are then likely to delay Brexit by up to three months in a further vote scheduled for later this week.
Deal or no deal?
Some British lawmakers had warned their Brexit-backing colleagues ahead of Tuesday's vote that rejecting the deal could lead to Britain's departure being postponed indefinitely, because a delay would give momentum to opponents of Brexit.
Calling for a further referendum, Plaid Cymru's Liz Saville Roberts argued the PM "must now accept that Parliament has rejected her wildly unpopular deal, so it is time to turn with respect to the public".
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It is also likely to increase pressure on Mrs May, who faced calls from members of her own party to quit or call a general election to break the impasse.
Juncker said he recommended the deal to the EU Council, which represents member states, and that Irish Prime Minister Leo Varadkar was prepared to back the changes on the backstop.
Pro-Brexit protesters on College Green, opposite the Houses of Parliament, in London.
"No deal must be taken off the table".
And German Chancellor Angela Merkel said Tuesday that the European Union was making "far-reaching proposals that take into account the concerns of Great Britain and to find answers for them".
Mr Cameron originally called the European Union referendum in 2016 as promised in his election manifesto.
Boris Johnson, the former Foreign Secretary who quit over Mrs May's tactics, said the premier's plan had "reached the end of the road".
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Less than 24 hours before the vote, May flew to Strasbourg, France, to meet with European Commission President Jean-Claude Juncker to hammer out enough changes to the deal to secure its approval from Parliament.
If that fails, they will vote Thursday to request an extension for the EU's two-year exit procedure.
He said there remained a "legal risk" that Britain could indefinitely remain in a "backstop", created to prevent a hard border on Ireland. May could also move to delay the exit until June if her deal is rejected again.
It comes after Attorney General Geoffrey Cox warned that, while the PM's last-minute agreements with Brussels "reduce the risk" that the United Kingdom could be trapped indefinitely in the backstop, they do not remove it altogether.
The pound rose more than half a percent to the day's high of $1.3155 at the London open, putting the currency about half way between this week's lows of $1.2945 and its high of $1.3290.
"I am very, very suspicious and concerned about the time scale", Conservative lawmaker Andrew Bridgen said.
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C'est un match décisif et nous ne voulons prendre aucun risque ". "On en saura un petit plus après l'entraînement de ce soir". Comme attendu, son remplaçant se nomme Philippe Coutinho , plus expérimenté mais moins en forme que le Français.
A government minister said the outcome was awful and warned the Conservative Party could split. "To do what? Because the... negotiation is finished, we have a treaty, it's there", he said, holding up the 585-page document.