He made his remarks alongside two other ex-taoisigh, Bertie Ahern and John Bruton, at a special Brexit conference in Dublin. Together, the three men oversaw government for more than 17 years.
Mr Cowen also directly criticised British prime minister Theresa May, telling the audience her inconsistent approach to Brexit and the negotiations was unhelpful.
Mr Cowen, who served as taoiseach from 2008 to 2011, pointed out that the EU wanted to ensure that non-membership or any State leaving it was “not going to be a burden-free zone”.
Brussels wanted to “try and ensure integrity of the single market” was maintained, he said.
However, that did not mean Ireland had to develop “an acrimonious relationship” with Britain. Nonetheless, with no solution in sight for the Irish question amid ongoing Brexit talks, the former Fianna Fáil leader maintained that there now “needs to be some flesh on the bone”.
Three options face Britain on the North, and the Government has now set a new deadline of June for any resolution to be on the table.
Otherwise, a so-called ‘backstop’ clause would allow the North to remain in the EU’s customs union and single market. London has still to offer a resolution.
Mr Cowen also dismissed recent Tory calls to scrap or change the Good Friday Agreement.
“It has not been fully implemented,” he said, referring to the rights of people in the North and the terms of the agreement.
He said Ireland changed its Constitution on the basis that there would be fairness, there would be equality and recognition of civil and cultural rights. There was a substantial amount of people with an objective of a united Ireland and this was “not subversive”.
“We have agreed to a compromise here that needs to be implemented and the rights of those who have as strong a nationalist aspiration as I have must be recognised,” said Mr Cowen.
“We have all agreed to get on a train. Up to the Good Friday Agreement, we were all concerned about the destination of the train. Now we are just agreed to go on a common journey and we are prepared to be agnostic about where the train will bring us once we are together and we are not beating the head off each other on the train.”
People should be entitled to be Irish as much as British in the North and that respect, embedded in rights legislation, should be finally given to the nationalist community, he argued.
Mr Cowen questioned Ms May’s approach to the Brexit talks after a series of flip-flops by Downing Street on a solution to the impasse on the North, including on the special deal to avoid a hard border.
“This level of inconsistency in terms of the approach doesn’t help to instil confidence that we can get a solution,” said Mr Cowen.
Former European Commission president Jose Manuel Barroso told the conference that Britain could not pick and choose bits of EU membership with Brexit.