"We want to bring the negotiating process forward", she said.
The Cabinet minister said service agreements almost always allow "some mode for movement that goes with that" but that was a "million miles away" from European Union free movement.
Davis was replaced Monday with Dominic Raab, a lawmaker who strongly supports Britain's European Union exit.
After the hours-long meeting at Chequers, May seemed to have persuaded the most vocal Brexit campaigners in the cabinet, including Davis, to back her plan to press for "a free trade area for goods" with the European Union and maintain close trade ties.
The EU has issued a veiled warning that it will not budge on its red lines after Theresa May unveiled her long-awaited Brexit plan.
Trump has sided firmly with Brexiteers, saying what May proposed would hurt the chances of a future trade deal between the United Kingdom and the US.
Without the backing of her own ranks and with a working majority of just 13, the prime minister will need to rely on opposition parties, Politico reported.
The PM insisted that the deal she agreed with her Cabinet at Chequers last week "delivers on the vote that people gave on Brexit" in the 2016 referendum.
Trump's Brexit comments came on the same day May's government published long-awaited proposals for Britain's relations with the European Union after it leaves the bloc next year.
The slew of resignations could possibly point to members of Parliament demanding a vote of no confidence in May, even though her team is confident that their Brexit plan would pass if it gets put to a vote.
"I developed a very close personal rapport with him, we worked closely together on many regional and global challenges and developed a strong friendship", she said. "That is exactly what we will do".
US Embassy issues warning of possible Trump protest violence
Gatherings and rallies are planned across the United Kingdom from Thursday, when Mr Trump is expected to touch down in Britain. According to The Guardian , Trump's itinerary will largely keep him away from the capital city.
This week she's had two high-profile departures from her Cabinet but it's more than just missing Boris Johnson and David Davis that she needs to be anxious about.
"I think you are losing your culture", he said.
Trump also had harsh words for current London Mayor Sadiq Khan, a fervent critic of the president, saying Khan "has done a awful job" running Europe's third-largest city.
Mr Trump went further and suggested to the Sun Mr Johnson was "a great representative for your country".
Europe s chief negotiator Michel Barnier said Tuesday talks will resume next Monday as scheduled with the new Brexit minister, while refusing to comment on the political infighting consuming London.
Britain is now part of the EU's single market - which allows for the frictionless flow of goods and services among the 28 member states - and its tariff-free customs union for goods.
Boris Johnson (pictured in London yesterday) has said he "just wants to get out of the EU" and that Britain can worry about the details "later" a former No10 aide has said.
Free trade would not apply to services, which account for 80 per cent of the British economy.
But he warned he felt "very strongly about the future of my country" and said Tories had "real concerns" about the direction of Brexit.
Anti-Corbyn MPs are likely to be annoyed by Davis and Johnson jumping ship, with many concerned it now leaves the door wide open for the Labour leader.
Rumours have swirled over possible further cabinet resignations but experts said May appeared to have weathered the crisis for now.