His remarks - ridiculed by pro-EU MPs - came after cabinet minister Matt Hancock said the government is increasing its refrigerated capacity to stockpile medicines as a precaution for a no-deal Brexit.
Speaking to Radio 4's Today programme, Mr Davis also increased the pressure on Theresa May to publish the government's full legal advice on any Brexit deal agreement to both cabinet ministers and parliament.
The Tory MP, who resigned from the government over Ms May's blueprint and said he would vote against it, claimed it is "looking like a probability" the prime minister's deal will fall if MPs are asked to vote on it in the coming weeks.
But, he added, this would result in renegotiating the deal with Brussels in a "slightly different atmosphere" with both the UK and the EU "staring" at the possibility of a no-deal.
He continued: "I don't think and I've said publicly, I don't think a no-deal is as frightening as people think, but the government is obviously nervous of it and the European Commission and nearly all member states are nervous of it. So I think that would force a very, very different, and actually, I think, rather better deal."
Asked about a no-deal, Mr Davis said there would be "some hiccups in the first year" but the UK would have "all the rights and controls over our own destiny."
"We're a big country, we can look after ourselves," he added.
Pressed on the publication of the government's legal advice - regarding any deal Ms May will present to the cabinet - Mr Davis said that while it is "convention" the legal advice is not released to the public, he added it is the "biggest decision" the current cabinet and parliament will make.
He said: "What we must see is the complete legal advice - not a summary, not something which just glides and glosses over all of the different issues, but the actual legal advice.
"He [attorney general] should provide the advice to the people who make the decision. Normally, that's the cabinet... there is no argument whatsoever on convention or on common sense or on tactic to withhold it from the cabinet and in my view from parliament as well."
Jacob Rees-Mogg, the Conservative MP who chairs the Eurosceptic European Research Group, said the information should "certainly be made available" before ministers sign up to any deal.
But on Wednesday, Mr Hancock, the health and social care secretary, insisted it is "not normal" for government to publish full legal advice, adding that a decision to do so would be one in "exceptional circumstances" by the prime minister.