The Tánaiste said Ireland had been through an economic and social crisis since 2008 and that trust in our institutions had taken a battering.
She said that efforts to reform and restore belief in society should include the Constitutional Convention becoming a regular feature of public life in Ireland.
The 100-member panel has finished its work but its recommendations have set in course a number of votes next year, including on same sex marriage.
The Labour leader told the MacGill summer school in Glenties, Co Donegal, that Irish citizens had seen “a major erosion of trust in the institutions that dominated the first 90 years of this State”.
This included scandals that surrounded the Catholic Church and the “reckless greed” of financial institutions. Rising inequality among citizens had also contributed to this, she told the audience.
Other referendums next year include reducing the voting age and reducing the age of candidacy of the President. Further referendums may follow on foot of other recommendations from the Convention.
Ms Burton suggested more reforms could be proposed by Irish citizens.
People would believe again in major institutions if they had a say in shaping their reform, it was added.
“We could make the Convention a regular feature of public life, so that every five years, or every decade, the Constitution would be reviewed in a methodological way and the public would have their say in that process,” she said.
Irish Examiner columnist Gerard Howlin said that Irish people were, in part, to blame for the country’s mistakes.
“Personal responsibility is largely evaded, because in our institutions, responsibility is porous,” the former government advisor said.
“Industrial schools, Magdalen laundries, mother-and-baby homes, bigger mortgages based on ever higher multiples of wages, a relentless demand for higher wages to fund them and ever greater levels of public spending to sustain the lot, were all founded on popular demand.”
Meanwhile, Ms Burton has called on Israel to pull back from its onslaught in the Palestinian coastal enclave of Gaza in the Middle East and for both sides to immediately agree on a ceasefire.
“The critical issue is to establish a sustainable ceasefire. That requires both sides to stand back,” said Ms Burton.
“Commitments by Hamas in relation to rockets being fired into Israel, but above all else that the Israelis would stand back from some of the actions that they have taken so that a viable ceasefire can actually be set in motion.”
This was needed to end the “appalling violence, death and carnage in Gaza”.
“Given the density in Gaza, there is no other safe place for a lot of the civilians involved to go to,” said Ms Burton.
“That is critical that the Israelis acknowledge that, that they stand back from what they’ve being doing.”