The Government says its reviewing its options following yesterday's surprise defeat in the Seanad Referendum.
The electorate voted in favour of saving the Upper House of the Oireachtas 52%, rejecting the Taoiseach's plan to abolish it.
Fianna Fáil leader Micheál Martin said the electorate had prevented a "power grab" which would have been the biggest ever amendment to the Constitution.
Taoiseach Enda Kenny, in what could be a hint at future reform, is insisting that change is still needed.
"This is the first time in over seven years that the people were asked a question - a direct question -in respect of the Seanad, and they've given their verdict. And I accept that," he said.
"I think there is one thing that everyone can agree on in the course of these particular campaigns … and that is that there's a continuous need for change and reform in politics."
Fine Gael are closing ranks behind the Taoiseach after the defeat.
Paschal Donoghoe, the Minister for European Affairs, has rejected accusations that the absence of the Taoiseach and top ministers from the debate affected the outcome.
Instead, he attributed the 52% No vote to the deep caution with which Irish people approach changing State institutions.
Fine Gael TD Simon Harris says Enda Kenny's reputation will not be affected, and the people will vote on economic issues in the next general election.
Establishing the new court of appeal, which was approved by the public in yesterday's second referendum, should take less than a year.
The Government will now move to set up the court after Friday's referendum on the issue passed with a clear majority.
Almost two-thirds of the country voted to favour of the new court.