The Commons will vote later on whether to give MPs a decisive say on any final deal struck with the EU in the autumn.
Mr Davis said Parliament would be involved in the process but could not undo the 2016 EU referendum.
The government was hit by a resignation ahead of the vote, with Phillip Lee saying Parliament was being sidelined.
The justice minister announced he was quitting over the Brexit strategy being pursued and that he could not support “how our country’s exit from the EU looks set to be delivered”.
MPs are gearing up for two days of votes on changes made by the House of Lords to the EU Withdrawal Bill. The most tightly-contested amendment is expected to be a call for Parliament to decide what happens next if it does not like the UK-EU Brexit deal.
Mr Lee cited the government’s opposition to this position in a statement on his website, saying it “breaches such fundamental principles of human rights and Parliamentary sovereignty”.
Theresa May has warned that any defeats on this key piece of legislation would send the wrong message to Brussels.
BBC political editor Laura Kuenssberg said the numbers were still “rather dicey” for the so-called meaningful vote amendment.
One of the potential rebels, former Attorney General Dominic Grieve, has tabled his own amendment which he said offered a “solution which would satisfy everyone” saying he “might well” vote against the government if it was rejected.
Speaking on BBC Radio 4’s Today programme, Mr Davis said a Parliamentary vote on the Brexit deal did not give “the ability to reverse the decision of the referendum”.
Asked what would happen if MPs rejected the deal, he said there would be no time to restart negotiations, with the UK leaving the EU in March 2019.
“If they throw it out, well they throw it out,” he said.
A showdown over customs seems to have been averted after a compromise amendment was accepted by the government – which means it has agreed to report to Parliament by October on efforts to negotiate a “customs arrangement” with the EU after Brexit.
The fallback position has won the backing of a cross-section of leading Tory MPs on either side of the Brexit argument, avoiding for now a showdown over calls – backed by the House of Lords earlier this year – for the UK to remain in a fully-fledged customs union with the EU after it leaves.
Mr Davis said a “great deal of progress” had been made in negotiations, saying he was expecting both a withdrawal agreement and the “substance” of the UK and EU’s future relationship to be finalised in October.
He also described as “nonsense” reports he threatened to resign over the wording of last week’s “backstop” plan to avoid border checks in Northern Ireland.
A big week for Brexit
The EU withdrawal bill is the legislation aimed at ensuring the UK has a smooth transition out of the EU, and will mean EU law is no longer supreme in the UK.
To avoid a sudden “cliff edge” on Brexit day, 29 March 2019, it would also convert existing EU law into UK law so the government and Parliament can decide at a later date which bits they want to keep or change.
The House of Lords has put forward 15 specific changes to the bill, but the government wants to kill off most of these changes.
However, numbers in the House of Commons are finely balanced, with the Conservatives not having a majority and needing the help of Northern Ireland’s Democratic Unionist Party to get their way.
To rebel or not rebel?
On Monday, Mrs May told her MPs they “must think about the message Parliament will send to the European Union this week”.
“I am confident I can get a deal that allows us to strike our own trade deals while having a border with the EU which is as frictionless as possible,” she said.
“But if the Lords amendments are allowed to stand, that negotiating position will be undermined.”
It is not yet known whether ministers will support Mr Grieve’s amendment.
Rebels have dismissed the government’s version, a commitment by ministers to make a statement within 28 days should MPs vote down the package negotiated by Mrs May.
Labour, which is backing 14 out of the 15 amendments, is urging Tory rebels to seize the chance to “decisively shape the course of the negotiations”.
Jeremy Corbyn’s party is also divided on Brexit, with several MPs unhappy Labour is not backing a bid to keep the UK part of the EU’s single market, like Norway.
Laura Kuenssberg: Squeaky moment or not?
There is still a chance of a squeaky moment for the government, or having to rely on votes from some Labour MPs, on a move to give Parliament more power if MPs vote to reject the final Brexit deal.
Sources tell me the numbers are still rather dicey for that so called “meaningful vote” amendment that will take place tomorrow.
There are discussions ongoing among potential rebels about whether they should deploy their forces.
Some of them believe, as they do on the customs issue, that they have the numbers to beat the government if they decide it’s the right moment. Appeals for party unity in the last couple of days, and the compromise on customs seem to have had some sway.
The key dates ahead on Brexit
What MPs will be voting on
The government opposes the following Lords amendments:
- Granting new powers to oversee changes made to EU law by the government
- Removing the precise day of Brexit from the wording of the bill
- Removing a section allowing ministers to use secondary legislation to establish when individuals can challenge the validity of retained EU law after exit
- Only let ministers use delegated powers to amend retained EU law where “necessary”
- Preventing ministers from using delegated powers to implement the UK-EU Withdrawal Agreement
- Make staying in the European Economic Area, like Norway, a “negotiating objective” for the UK
- Transferring the EU’s Charter of Fundamental Rights into UK law
- Allowing “enhanced scrutiny” when ministers use delegated powers to change EU employment, equality health and safety, consumer and environment rules
The government has proposed its own version of these ones:
- Giving Parliament the power to decide what happens if MPs and peers reject the final Brexit deal
- Explicitly preserving cooperation between Northern Ireland and the Republic and commit to no new border arrangements without the agreement of the UK and Irish governments
- Allowing people to challenge UK law if it fails to comply with the general principles of EU law
- Forcing ministers to maintain EU environmental principles in domestic law after Brexit
- Compelling ministers to aim for a deal allowing unaccompanied child refugees to join relatives in the UK
The government has accepted this amendment:
- Allowing the UK to replicate EU law made after Brexit day and continue to participate in EU agencies
The government is backing a compromise backbench amendment on this:
- Forcing the government to report on “steps taken to negotiate a customs union with the EU” by 31 October