At the 1922 Committee, she is understood to have warned MPs that Jeremy Corbyn will end up in power unless she receives their support.
Sky News understands that there was no mention of Mr Johnson or Mr Davis at the meeting.
They resigned days after the entire cabinet – the foreign secretary and Brexit secretary included – signed off on the PM’s plans to create a UK-EU free trade area.
On Sunday night, Mr Davis was the first to step down – admitting he had become a “reluctant conscript” to the agreement made during the Chequers awayday.
Mr Johnson, who reportedly described the plans as “a big turd”, then announced his resignation this afternoon. In a letter to the prime minister, he said the UK’s Brexit dream is “dying – suffocated by needless self-doubt”.
Downing Street is expected to announce the foreign secretary’s replacement in the coming hours.
Speaking in the Commons, the prime minister paid tribute to the departing ministers.
Mrs May said that both men had made important contributions to the UK, but had not agreed with her about “the best way” of delivering Brexit.
She praised Mr Davis for his efforts in establishing the Department for Exiting the European Union, and said he had steered through some of the “most important legislation for generations”.
Meanwhile, the prime minister praised Mr Johnson for the “passion” he had shown in promoting a “global Britain to the world”.
In the terse statement, Mrs May defended her Brexit plan, which had received collective agreement from the cabinet just three days ago.
The proposal commits the country to maintaining the same rules as the bloc for goods and agricultural products, something eurosceptics fear could result in a “soft Brexit”.
She warned it was the “only way to avoid a hard border” between Northern Ireland and Ireland – and Mrs May urged the EU to take her proposals seriously.
The PM added: “What we are proposing is challenging to the EU. It requires them to think again and look beyond the positions they have taken so far and agree a fair balance of rights and obligations.”
Responding to her statement, Jeremy Corbyn said the Chequers agreement “stands as a shattered truce, a sticking plaster over the cabinet’s cracks in this government”.
The Labour leader claimed that the two ministers waited a few days to resign so they could catch a ride home from the PM’s country retreat in a government car.
He labelled the government as in “crisis” following the resignations, adding: “For the good of this country and its people, the government needs to get its act together and do it quickly and if it can’t, make way for those who can.”
Mrs May shot back, quipping: “He talks about resignations, can I just remind him, I think he’s had 103 resignations from his frontbench, so I’ll take no lectures from him.”
Sky political correspondent Lewis Goodall said the departures left Theresa May’s premiership “hanging by a thread”.
Mr Davis, who has been replaced as Brexit secretary by Dominic Raab, said it looked “less and less likely” the Conservatives would deliver on the Brexit result and their commitment to leave the EU’s customs union and single market.
Following his departure he claimed he had no desire to weaken the prime minister, but warned the UK is giving “too much away, too easily” in Brexit talks.
Former UKIP leader Nigel Farage welcomed Mr Johnson’s decision to resign, saying it was time to “get rid of the appalling @theresa_may and get Brexit back on track.”
Mr Raab, a Brexiteer who takes over the role of negotiating with Brussels the detail of the UK’s Brexit agreement, previously worked in the Ministry of Housing, Communities and Local Government (MHCLG) under the secretary of state James Brokenshire.
His job will be to convince the European Union – whose negotiators are led by Michel Barnier – that the PM’s plan for a new UK-EU free trade area for goods provides the best framework for a relationship after Brexit.