It's like a family loss - Robinson
The human rights campaigner, who worked closely with South Africa's first black president, lauded his sense of humour, describing him as "a huge flirt".
"Why is it that we celebrate that we are so sad, that we feel a loss as if it's a family member?" Ms Robinson said.
"Why are we so bereft?
"Because he was the best of us. He was the best of our values."
Ms Robinson, Ireland's first female president, attended Mr Mandela's inauguration in 1994.
They continued to work closely over the years and in 2007, Mr Mandela appointed the campaigner to The Elders - an independent group of global leaders who work together for peace.
Ms Robinson said the leader wanted the values that inspired his country to become a "rainbow nation" to help create a "rainbow world".
"He lived the values he talked about," she told RTE Radio.
"His long walk to freedom, the struggles he made, the reconciling, the peace that he made when he came out of prison, he wouldn't negotiate until he came out of prison.
"So instead of the apartheid government being able to somehow manipulate him, he completely controlled the discussion of forming a government.
"So he was very strong, but he was also very human."
Ireland's current president, Michael D Higgins, said Mr Mandela's "powerful" example will go on after his death.
He described the leader as "very, very impressive, in every sense".
"When he spoke on the last occasion, he spoke about the importance of a future devoted to peace," Mr Higgins said.
"He had that phrase, which occurs regularly in his speeches, about the struggle for freedom and achieving the right to deliver freedom."
The one-time Irish Anti-Apartheid Movement expressed sadness at the death of Mr Mandela.
The group, which disbanded in 1994 after 30 years, described him as "the greatest man of the 20th century".
"Sufficient for us to say that his incorruptible integrity, his humanity and his generosity of mind and spirit were always the lodestar in light of which we strove to run the movement," it said in a statement.
"We feel privileged to have had the opportunity to contribute in some small way to the historic and valiant struggle for democracy and freedom for Madiba and his cruelly oppressed people in South Africa."
Sinn Fein president Gerry Adams said Mr Mandela was his hero.
He said Ireland stands to learn a lot from the peacemaker, whom he insisted showed loyalty to the republican movement in the 1990s.
"In the hard years when the western powers were against him, when he was vilified as a terrorist and a criminal, he kept the faith," Mr Adams said.
"He showed by perseverance and vision how to build peace out of conflict, a better and more equal future based on fairness, and unity out of division."
Books of condolence opened across the country for Irish people to pay their respects.
Leinster House in Dublin, which is home to the Irish Parliament, flew its flag at half-mast to mark Mr Mandela's death.
Meanwhile, a string of religious figures paid tribute, including Bishop John McAreavey, chair of the Council for Justice and Peace of the Irish Episcopal Conference.
"Through courageous self-sacrifice Mandela led people to freedom in the fullest sense of the word - the lasting, spiritual freedom that can only be achieved through reconciliation and forgiveness," he said.
"He was a true visionary and a powerful advocate for the need to engage in the harsh realities created by conflict in a spirit of truth, justice and human rights."