Mr Durkan however said there questions to answer about the integrity of the EU referendum.
He was speaking after calling on the Irish Government to convene an urgent all-Ireland, all-party forum to examine the implications of Brexit for the whole country.
Mr Durkan said: “People in Northern Ireland, who made a sound judgement, have a right to say: ‘We shouldn’t just be led into whatever happens next by people who don’t have a clue and don’t have a mandate.’
On the issue of a reunification border poll, Mr Durkan added: “The uncertainty would be compounded and would multiply by a border poll at this time. It is not the answer.”