Taoiseach Enda Kenny has said there will be no re-run of the referendum on the abolition of the Seanad.
Mr Kenny was speaking after the electorate voted by a narrow margin not to abolish the upper house.
Asked about his decision not to debate the issue in advance of Friday's vote, Mr Kenny said everybody had their personal opinions and it was immaterial to the outcome.
Speaking in Co Sligo, the Taoiseach said: "People love to have shouting matches.
"We know now that like the All-Ireland Final, it is not going to be replayed so we have to deal with the question of how you make a Seanad effective."
Mr Kenny would not be drawn on whether the outcome was damaging for him. He said he had other serious business to attend to, including the Budget.
Meanwhile, the Reform Alliance is to seek the suspension of normal Dáil business tomorrow to discuss Seanad reform.
Speaking on RTÉ's Today with Sean O'Rourke programme, Reform Alliance TD Lucinda Creighton said the group hopes to be able to discuss the outcome of the referendum in order to assist the Government in Seanad reform.
She said: "It's important for all members of the Oireachtas ... to have an opportunity to feed into the process and help give the Government some guidance."
The alliance is made up of Fine Gael TDs and senators who lost the party whip.
Independent Senator Feargal Quinn said the Taoiseach and Government should now work with senators to bring forward proposals for Seanad reform.
Speaking on RTÉ's News at One, Senator Quinn said Mr Kenny should introduce a bill incorporating proposals by Independent Senators for reform.
He said their combined efforts could result in real change and reform.
Mr Quinn said: "He could do something that de Valera wasn't able to do, others weren't able to do - 75 years without change and we could have legislation in 75 days.
"We don't have to go to Constitution to do that. We don't have to change the Constitution. We don't need a referendum. We could have the perfect answer.
"Most parliaments get together and people from different parties get together. I think that's what we have to do first thing. We have to work on that and see if we can get our thoughts together."
Adams stands over Sinn Féin position
Sinn Féin President Gerry Adams has said he stands over the position the party took on the Seanad referendum, and accused the Government of running a "ridiculously dismal campaign".
Mr Adams also criticised the Taoiseach for not debating the issue.
"This was a personal policy initiative by the Taoiseach yet he wouldn't debate the points. Sinn Féin was one of the very few parties who actually canvassed on that issue," he said.
Speaking on RTÉ's Morning Ireland, Mr Adams said he did not regret Sinn Féin's stance but said the Government would not listen to the party's advice to make Seanad reform part of the Constitutional Convention.
He said the Sinn Féin position had been vindicated and that other political parties were now arguing for reform.
Asked whether he personally had been visible enough during the campaign, Mr Adams said he had challenged Fianna Fáil leader Micheál Martin to debate.
He also questioned why he had not been invited by RTÉ to be part of a televised Prime Time debate.
Mr Adams said he personally was in favour of abolishing the Seanad, after the Government would not take account of Sinn Féin's proposal for root and branch reform as a referendum choice.
FG chairman blames savings claims
Fine Gael Chairman Charlie Flanagan said claims that the abolition of the Seanad would save €20m were much more contentious than the Taoiseach not participating in a television debate.
Also speaking on RTÉ's Morning Ireland, Mr Flanagan acknowledged that the defeat of the referendum vote was a setback for the party and "the damage must be assessed".
Mr Flanagan said there was more than one reason why people voted No, and the Taoiseach's refusal to debate was not as important as some were saying.
Mr Flanagan said it would be very disappointing if the issue of Seanad reform eclipsed the larger issue of Dáil reform.