"You can not carry out this negotiation on the basis that every aspect of it is going to be negotiated with the DUP to get their vote in support of it and then you are going to try and get the entire Conservative Party to agree with each other on whatever you have tried to negotiate", he told BBC Radio 4.
The DUP campaigned for Brexit but is mindful 56% of people in Northern Ireland voted Remain.
But several Labour figures have suggested that Britain could strike a deal to access European Union markets on the same basis as now - meaning mass immigration might continue.
The embattled 60-year-old premier said she had served the Conservative Party since the age of 12 and will continue to do so as long as she is wanted.
Ireland's Prime Minister Enda Kenny has warned May that deal might endanger peace. She has said she wants a "frictionless" border with Northern Ireland.
Prior to the election, Ms May had said that the United Kingdom would be leaving the single market and the customs union and she repeatedly insisted that "no deal is better than a bad deal".
'The DUP will accordingly support the Government's determination to maintain the scope and reach of our diplomatic effort, the scale and effectiveness of our global aid programme (including in relation to conflict resolution and stabilisation) and the strength of our national defence.
European Union leaders have voiced growing impatience to start Brexit negotiations, which have already been delayed by the parliamentary election - and on which the clock is ticking. "The intent is to ensure that we have the stability of Government in the national interest".
As such, the DUP may seek enhanced borrowing powers or flexibility on budgetary controls rather than hard cash. While it wants more representation in Westminster, including a permanent Northern Ireland secretary in the cabinet, it is also calling for devolution to be respected by London.
In the draft, the Tories promised to "enhance" foreign office support for foreign direct investment into Northern Ireland.
Foster will nearly certainly ask for greater investment in Northern Ireland as part of the deal, as well as guarantees on support for pension plans and for winter fuel allowances for older people. It is also against any move to limit those who can receive the winter fuel allowance. For every myth about EU nationals taking jobs and lowering wages I will consistently cite the huge amount of research which shows the huge benefit people from other European countries bring to Britain.
The situation has seen Irish leaders call for a "special status" for Northern Ireland after Brexit. The Tories have already pledged to increase the minimum wage and the personal tax allowance. Thus we must begin this negotiation.
The 10 members of the DUP remain outside but supportive of the Government.
The DUP also wants a UK-wide definition of a victim that excludes perpetrators killed or injured while carrying out violent acts.
Without a so-called confidence and supply deal with the DUP, her party risks losing the vote next week on the Queen's Speech, which lays out the agenda for the government.
Having helped deliver a number of major events to Northern Ireland, such as the Giro d'Italia and golf's Open Championship, the DUP may ask for support hosting other high-profile global show-pieces.
Likely Government response: One-offs like this could well be offered up by the Government although Armed Forces Day may prove controversial in Northern Ireland.
Many of those are couched in vague discursive terms rather than as firm commitments, something which nearly certainly has changed in this negotiation, given the strength of the DUP position after last Thursday.
However, it is unlikely these will feature in the negotiations with the Conservatives.
Power-sharing talks failed following a snap election last March.