Mr Corbyn, in his reply, said: "I do have sympathy with the Prime Minister on her voice and I hope it soon recovers, I understand how painful this is".
MPs will vote on Wednesday evening on whether to reject a no-deal Brexit.
And the vote was later confirmed by a more emphatic 321 votes to 278 when the Government's motion was put forward as amended.
Their amendment seeks to prevent the country leaving the European Union on March 29 if the government has not agreed a "deal" to leave.
Mrs May said MPs would have to decide whether they want to delay Brexit, hold another referendum, or whether they "want to leave with a deal but not this deal".
Mrs May reiterated votes are planned on a no-deal Brexit and extending Article 50, adding: "There will be hard choices for this House but this House will need to determine what its view is on the way forward".
"A bad deal would be even worse than no deal, but best of all is a good deal, and this is a good deal", the prime minister told the sombre Commons chamber.
In total, 391 MPs voted against the deal and 242 backed it.
But Speaker John Bercow told her it was not possible for her to withdraw the amendment, as one of its other signatories could move it to a vote.
Jacob Rees-Mogg, chairman of the European Research Group of Brexiteer MPs, said he felt the rejected deal had not delivered on the commitment to leave the EU cleanly and that the backstop would have kept the United Kingdom in the customs union.
MPs who voted against: Mr Kyle (Hove), Ms Lucas (Brighton Pavilion), Mr Russell-Moyle (Brighton Kemptown), Mr Smith (Crawley).
'In practical terms the only way no deal can be stopped is by revoking Article 50 or agreeing a deal.
There will be an urgent question from Labour in the Commons later, asking Mrs May for an update on the progress made in achieving legal changes to the withdrawal agreement and the timetable for its approval.
Mr Loughton tweeted: "This evening I have held my nose and voted for the Government's deal with the Attorney General's extra assurances with no enthusiasm but with a greater fear of the damage that prolonged uncertainty and chaos could cause but I fear with little chance of it going through".
Theresa May has confirmed she will vote to block a no-deal Brexit at the end of the month, as she faced renewed pressure from Jeremy Corbyn to abandon her "dead" departure plan and instead embrace Labour's customs union alternative.
Shadow business secretary Rebecca Long-Bailey told BBC News Parliament would increasingly "set the agenda" if the government was not in control of events.
Speaking in the Commons he called on Parliament to "take control", saying Labour would take part in cross-party talks to find a "compromise solution" with 16 days to go until Brexit day.