Asked if there should be a second referendum, Mr Cameron added: "What happened last night is some people who've always wanted Brexit have voted against it again and this is exasperating for the Prime Minister".
If no-deal is rejected, MPs will vote on Thursday on delaying Brexit by extending Article 50 - the legal mechanism that takes the United Kingdom out of the EU.
EU Withdrawal Agreement: how MPs voted.
Lewes MP Maria Caulfield and Tim Loughton, East Worthing and Shoreham MP, both voted against the first deal in January, but backed Mrs May's revised withdrawal agreement last night (Tuesday March 12).
"The deal doesn't deliver what my constituents voted for, whether they voted to leave or remain".
An extension to Article 50 can only be granted by unanimity among the 27 remaining European Union member states, and Brussels has made clear they will do so only if the United Kingdom presents a "credible" justification for being given more time.
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". We are not doing what we need to do, which is govern the country effectively and properly.
Downing Street has so far not laid out any groundwork for an extension.
On Monday (March 11), the Labour MP led a debate in Parliament calling for Article 50 to be revoked.
Conservative MP John Baron then pushed Mrs May to back a no-deal Brexit, arguing "no deal is better than a bad deal".
Chancellor Philip Hammond used his Spring Statement to call on MPs to "put aside our differences and seek a compromise", warning the United Kingdom would face "significant disruption" from a no-deal Brexit. "It is not sustainable, the current situation in parliament", he told BBC Radio 4′s World at One programme.
"Ultimately, when you look at the alternatives - which are a customs union, no Brexit or no-deal - Theresa May's deal is more attractive than those other three options".
On Wednesday morning the government announced that most imports into the United Kingdom would not attract a tariff in the event of a no-deal Brexit.
SNP MPs have reiterated calls for a second referendum, saying that the time has come for May to accept that a new referendum is necessary.
"I might sound arrogant but I thought it was very important to think it through: 'Can I cope with it?"