A Government minister believes Taoiseach Enda Kenny should have taken part in a TV debate to fight for the abolition of the Seanad.
Communication Minister Pat Rabbitte said while the Government must now try to reform the upper house, he was left "scratching his head" about what reform meant.
Almost 52% of the electorate voted to keep the Seanad, with the Taoiseach admitting he was left personally disappointed after his Government suffered "a wallop".
His role in the campaign was defended by Mr Rabbitte, who insisted Mr Kenny did debate in the Dail and wherever else it was raised.
"The only issue is he didn't do the debate (on television)," Mr Rabbitte told RTE.
"I think my own view is he should have done it."
The result was deemed to be an embarrassing and damaging blow to Mr Kenny, who spearheaded a campaign to scrap it.
The Taoiseach has said the Government will take time to reflect on the decision and on what role the upper house will play in his agenda for political reform.
Mr Rabbitte said senators had admitted during the course of the campaign that the present Seanad was dysfunctional and irrelevant, and politicians now have an obligation to reform it.
But the former Labour party leader revealed that would be difficult to do that without another referendum.
"It will take some discussion and some debate about how that can be done within the constraints of the constitution and without another referendum," Mr Rabbitte added.
Party colleague Brendan Howlin also said a second referendum may be needed to radically reform the Seanad.
The Minister for Public Expenditure Minister and Reform said there are some changes that can be made within the confines of the constitution to make both houses more effective.
"There are lots of ideas on reform, whether we can build a consensuses of exactly how the reform should be implemented I think is that immediate challenge," he said.
"Ultimately we may need to ask the people by way of another referendum for specific changes to bring about more radical reform than the current constitution provides for."