Video report by ITV's Political Editor Robert Peston
Arlene Foster has said the details of the UK's planned Brexit deal with the EU as "a big shock" to the DUP.
The Northern Irish party has said it was given details of Theresa May's planned offer to the EU on Monday morning, hours before the parties hoped to announce an agreement.
Mrs Foster said it quickly became clear that the offer was not acceptable, leading them to call a press conference which scuppered hopes of moving forward to trade talks.
Mrs Foster laid the blame for the eleventh-hour breakdown of a deal squarely with the Irish Republic.
According to the British negotiators, the Irish Republic had deliberately withheld details from Northern Ireland until the last minute, she claimed in an interview with the Irish RTE station.
"They are pushing at an agenda which leads a lot of unionists to think there is something else," she said.
When asked if she felt let down by Mrs May, she replied: "I said that it could have been dealt with differently."
She indicated that she was prepared to hold firm even if that risked a hard border inside Ireland - something that the Republic have said is a red line.
"Nobody wants to see a hard border, but the reality is there is a border. It's there because we're two different jurisdictions and I think some people need to be reminded of that sometimes."
Video report by ITV News Correspondent Juliet Bremner
It came as Irish Taoiseach Leo Varadkar said he was confident that a deal could be salvaged before the end of the year as he pressed the UK to come up with a solution.
"I look forward to hearing from them as to how they think we can proceed. The ball is now in London's court," he said.
Senator Neale Richmond, a senior Irish EU Affairs spokesman, said a hard border would be "a disaster for everyone" but his country could not be "bullied and forced into jumping the gun here".
Both countries in Ireland can be dealmakers over the Brexit process.
Ireland as a EU member can use its veto to block talks moving forward, while the DUP is propping up the Conservative Government in London and as such must be appeased.
Former Northern Ireland secretary Lord Hain said the scenes in Brussels had been a "car crash" which could have been foreseen by anyone with knowledge of Irish politics.
"Unionists were quite legitimately always going to insist that they could not be put in a status distinct from the rest of the UK," he said at question time in the Lords.
In the Commons, Brexit Secretary David Davis faced stinging criticism from MPs as Labour labeled the government's Brexit negotiations an "embarrassment".
Mr Davis was responding to an urgent question raised by his Labour counterpart Keir Starmer.
In a heated exchange, Mr Starmer called for the deadline of 29 March 2019 for the UK to exit the EU to be abandoned, and for options such as staying in the EU customs union "back on the table".
He also said the collapse of the talks showed that the "DUP tail is wagging the Tory dog".
Mr Davis defended the governments efforts in the talks, insisting that "progress has been made" and saying he believed the first phase of the talks was now close to concluding.
"All parties remain confident of a positive conclusion by the end of the week," he said.
He said the government had no intention of allowing "one part of the United Kingdom" to remain inside the single market and customs union when Britain leaves the EU.
"That is emphatically not something that the UK government is considering," he said.