The EU's other 27 member states will have a chance to examine and respond to the UK's Brexit white paper when its General Council of ministers meets in Brussels this morning.
"No technology solution to address these issues has been designed yet or implemented anywhere in the world, let alone in such a unique and highly sensitive context as the Northern Ireland border", she said.
The meeting on Friday was also the first chance for ministers to talk about the so-called white paper , key proposals on the future relationship drawn up by British prime minister Theresa May, which have already been undermined by hardline Brexiteers in parliament, by amendments to a trade bill, as well as the resignations of foreign secretary Boris Johnson and Brexit secretary David Davis.
May insists that the notion of a hard border is nearly inconceivable.
Speaking after meeting the Tory leader, the Dublin Central TD said: "We were told that the British prime minister came to Ireland to listen and to reassure - it is clear that she is not listening to community and business interests and seeks only to reassure the DUP".
"I made it clear yesterday to Dominic Raab that we are not asking for a border between Northern Ireland and the rest of the UK".
With a little more than eight months to go before Britain is due to leave the European Union on March 29, 2019, May's government, parliament, the public and businesses remain deeply divided over what form Brexit should take.
All outstanding problems - including the most controversial and intractable, the Irish border question - are supposed to be solved by October, when the European Union expects a final deal to be reached on what Brexit will look like, including the UK's ongoing relationship with Brussels.
Mr Grieve said he did not believe Mrs May is at risk, but added: "The only group that could possibly bring the Prime Minister down is if the group of my hard Brexit colleagues so lose the plot that they decide that is an effective way for them to proceed".
Barnier also said he would ask the British government whether the blueprint met the EU's guidelines, including on the movement of goods, capital, people, and technology, and if the draft supported the integrity of the EU single market and the autonomy of European decision-making.
He warned there would be "conditionality" under the Article 50 withdrawal mechanism between settling Britain's exit payment and creating a new relationship with the EU. Barnier said he had invited British negotiators to discuss the backstop next week.
Gerald Mason, senior vice president at Sugars, said told BBC Radio 4's Broadcasting House: "In theory the white paper allows the United Kingdom to have an independent trade policy, in practice the mechanism that will be used to jointly police the UK's and EU's tariffs is what we are confused about".
"We need to de-dramatise things", Mr Barnier said.
However, the 20% left is challenging to say the least - covering flashpoints like data protection, United Kingdom military bases in Cyprus and who should police the withdrawal agreement and subsequent nearly two-year transition period.
Prime Minister Theresa May agreed in December to a financial settlement totaling £35 to £39 billion ($46-51 billion, 39-44 billion euros) that ministers said depended on agreeing future trade ties.