Outlining why Chequers was worse than membership, Mr Davis added: 'We will be under the rule of the EU with respect to all of our manufactured goods and agri-foods, that's a really serious concession, what about take back control, it doesn't work.
'That actually leaves us in a position where they dictate our future rules without us having a say at all, so it's a worse deal.'
Mr Davis added: 'The other argument I made at that Chequers cabinet was this won't be the last step, they will not accept this.'
Reacting to Mrs May's statement that there won't be more compromises, he said: 'Except in the national interest... that is an incredible open sesame to all.'
On the Northern Ireland border, he added: 'I do think, I'm free to talk more freely now than perhaps when I was a minister, I do think we've heavily over-emphasised the problem on the Northern Ireland border...
'This is a much more straightforward issue to deal with if we choose to, if we put the political will behind it, we and the Irish Republic, the two together.'
Mr Davis argued Brexit was about facilitating trade with the rest of the world outside the EU.
He said: 'I said all along there'd be technical and tactical problems and there'd be pressure points and we'll have to live through the pressure points, we have to see the other side off in some respects here.'
He went on: 'I was always the Brexit Secretary, the question is whether I controlled events, that's another matter.'
He added: 'The reason I left after Chequers was we'd got to a point where her (Mrs May's) view advised by Olly (Robbins), but not just by Olly, advised by many others was different from mine.'
Asked if the Prime Minister believed Brexit would be a good thing for Britain he said: 'I think so.'
Earlier, Mrs May today ruled out giving in to calls for a second EU referendumwarning it would be a 'gross betrayal of our democracy'.
The Prime Minister said voters made their decision in 2016 by 52 to 48 per cent and that must be the end of the debate of whether Britain will leave the European Union.
Pro EU campaigners have spent the summer building momentum and resources behind a call for a new referendum once the Brexit deal has been negotiated.
The People's Vote campaign insists they want a 'first referendum on the facts' but it has enraged Brexiteers who say the issue has been settled.
Mrs May moved to close down the question today in comments revealed by the Sunday Mirror.
She said: 'I will not give in to those who want to reopen the whole question with a second referendum.'
'They trusted that their vote would count, that after years of feeling ignored by politics, their voices would be heard.
'To ask the question all over again would be a gross betrayal of our democracy - and a betrayal of that trust.'
