Minister for Finance Micheal McGrath has said the Government will have to "reflect" on whether the next budget should have specific measures to assist carers in light of the twin referendum results.
Speaking following a meeting of eurozone finance ministers in Brussels, Mr McGrath said: "The public wants to see more practical measures to assist carers and to reflect the level of priority that they attach to supporting carers in budgetary decisions.
"We will of course have to reflect on that. We have made a lot of progress in recent years, through different reforms and additional investment that we have made."
He said the biggest problem in the care sector in recent years has been the lack of staff, rather than a lack of budgetary support.
Mr McGrath said: "In too many instances where the budget is there to provide home care support, we haven't been able to find the staff.
"People are very much focused on their own lived reality, the day-to-day challenges that they're facing.
"The public genuinely wants to see the Government do everything we possibly can to support carers.
"That is a takeaway from the referendum. On that question, people felt that the wording just didn't go far enough and that's something that we have to recognize, accept, and try to deliver more tangible, practical improvements in the supports that are there for carers who do the State an incredible service."
Carer tax breaks
He said the idea of tax breaks for carers would have to be balanced with the need to run a "successful economy".
Having budget surpluses meant you could have resources to do new things on both the taxation and expenditure side, he said.
"On the taxation side, it is important for Ireland that we have a competitive personal tax system, that is a factor when investors are weighing up the relative strengths of different jurisdictions and where they have choices to make about where to invest.
"Even in recent budgets, the heavy emphasis in how we have allocated resources has been in favor of investment and expenditure in health and education and social protection. I expect that that will continue," he added.
He said investment in frontline services and practical supports would be prioritised, while there would also be resources for improvements in personal taxation.
"That's important not just in allowing people to keep more of the money that they earn, but it is a factor when investors are looking at the comparative strengths and weaknesses of different countries when they're making investment decisions."
Dept referendum statement 'an error'
Meanwhile, a spokesperson for the Department of Agriculture, Food and the Marine said a statement issued by the department last week calling for a Yes vote in the referendums "was an error".
On Wednesday, a press release titled 'Minister McConalogue advocates YES vote amongst the farming community' was sent from the departmental email account.
The department was not aware of the statement, a spokesperson said, adding that "the press release should not have been sent from a department account".
Under the McKenna judgement, public money cannot be used to advocate for one side of a referendum argument.
The Family and Care referendums were defeated at the weekend, with 67.69% and 73.93% of people voting against the respective amendments.
Referendum results a reflection of frustration - Fitzmaurice
Meanwhile, Independent Ireland TD Michael Fitzmaurice said that people are "frustrated" with the Government and the No vote in the two referendums was a result of people feeling that they were not being listened to.
Speaking on RTÉ’s Morning Ireland, he said that it comes down to a lack of trust in the Government.
"I think people are frustrated with Government that they're not being listened to. The Government, anytime they were questioned basically on the word 'durable', they weren't able to give a definition," he said.
He added that when documents or memos were sought for clarification, the Government response was that they would not be released until after the referendums.
We need your consent to load this rte-player contentWe use rte-player to manage extra content that can set cookies on your device and collect data about your activity. Please review their details and accept them to load the content.Manage Preferences
"It's not a good sign when a Government minister comes out and says that they're not going to release information until after the referendum was over. And I think people took the attitude basically, ‘if in doubt, leave it out’."
Mr Fitzmaurice said "there’s nothing wrong" with people opposing a Constitution amendment.
"This is our Constitution. People have a sovereign right and they have made their decision and everybody must respect that."
He said that if the referendums were to run again, he believes that there will be "a bad taste in people's mouth", like what the Lisbon Treaty referendum showed.
"I believe that now they should let it lie. Let it go, because what they have done, they haven't achieved what they set out to achieve and now the people have spoken. Respect the people, what they have said and move on."

Call for Govt to repay campaign costs
The Government should repay the taxpayers' money spent on the referendum campaigns, Senator Rónán Mullen said.
"You cannot hijack the apparatus and the resources of the State to push through an ideological agenda, which is what happened here," he said.
Speaking on RTÉ's Today with Claire Byrne, he said the entire political class had failed people.
"There needs to be a debate now about the way the insider political class is driving its agenda."
He asked if the Government would commit to recognising what the voters had decided about marriage and motherhood.
"And will they recognise that they need to call a halt to the culture war legislation?" he added.
Additional reporting Joe Mag Raollaigh