Foster said to regain the DUP's support May would have to remove the Irish protocol from the legally binding withdrawal agreement, something the European Union has repeatedly made clear it will not countenance.
"The disappointing thing for me is that the prime minister has given up and she is saying this is where we are and we just have to accept it", Mrs Foster told the BBC's political editor, Laura Kuenssberg.
For now Mrs May's message - in Northern Ireland as elsewhere - is that there is no alternative.
He called for the Government to "junk" the backstop - a plan that sees Northern Ireland remain in a customs union with the EU to allow for frictionless trade between the Republic and Ulster, while the rest of the United Kingdom opts out.
Ahead of the tour, she said: "Having been told by the European Union that we would need to split the UK in two, we are leaving as one United Kingdom".
The DUP is determined to prevent any divergence from the rest of the UK.
The DUP conference appeared more understated than in previous years.
Addressing her party conference in Belfast, Foster reiterated her rejection of the draft agreement.
A senior Tory MP told MailOnline said the votes were a signal the government might not last long even if Theresa May somehow managed to force her Brexit deal through Parliament.
"I make no excuses". So let's get rid of it.
The prime minister, who faces an uphill battle to get the controversial deal through Parliament, has been accused by the Orange Institution of "betraying the unionist community" in Northern Ireland.
Although they only have 10 MPs in the House of Commons, the DUP's support is vital in May being able to keep a majority.
Ms Foster said the constitutional implications of the deal could not be ignored.
The DUP has effectively suspended its "confidence and supply" arrangement with the Conservatives in protest at the backstop contained within the Brexit deal.
"The reality is that if we are to secure a better outcome than is now on offer then the only option is to look beyond this current draft withdrawal agreement", she added.
The rhetoric highlights the domestic challenges that lay ahead for Mrs May. "We're talking to people in the remain side, we're talking to Brexiteers, we're talking to everyone, as I think you would expect us to do".
Foster declined to say whether her party would remove its confidence and supply arrangement keeping May in power if the Brexit deal was passed by the Commons, saying only that she would "review" the issue in this case.
The DUP is threatening to reconsider its support of the Conservative government if Theresa May's Brexit deal passes.
But in a possible conciliatory offer, he added: "It is in the interests of the country and of Northern Ireland that our parties continue to work together in the national interest". "There will be much wailing and gnashing of teeth over the duplicity of the prime minister".
"Don't believe the propaganda that it's too late - it isn't".
She said: "We have been resisting numerous things the European Union had wanted to put".
"But it is not this deal". The Prime Minister used to say that.
Samantha Sacramento was given a rousing reception by DUP members as she insisted Gibraltar will not be "bullied" by any bid from Madrid to undermine its sovereignty.