Finance Minister Paschal Donohoe has admitted it is "bonkers and unbelievable" that women are losing out on pension payments due to a recent change in the rules.
Thousands of women are getting smaller pensions because they left the workforce before 1994 to care for children.
Others are taking a pensions hit because they once had a summer job or worked part time for a while.
It is estimated that 23,000 females have been hit with lower payments due to changes to State pension eligibility rules in 2012.
Changes made by then social protection minister Joan Burton in the previous government make it more difficult to qualify for a full pension.
Retired women are losing more than €1,500 a year on average, according to calculations by advocacy group Age Action.
The rule change also means that the women affected will not get the full €5 increase in the State pension announced in the Budget and due from the end of March.
Mr Donohoe admitted it was wrong that women were being affected in this way.
He was reacting to a caller to the 'Today with Sean O'Rourke' show, whose wife is losing money due to the change.
Eamon Tynan, a pensioner from Co Longford, said the situation was costing her €35 a week in her pension payments.
His wife had a summer job in the 1960s when she was a secondary school student before joining the civil service.
As a result, "her contributions are now averaged out and divided by 50", he said.
The problem was a "huge issue for women retiring around now in their 60s", Mr Tynan said.
The minister responded that it was "bonkers and unbelievable" that women who worked and obeyed the law by paying pension contributions were now getting lower pensions.
"I think it is wrong the way they were treated. It was wrong then and it is wrong now," he said.
Mr Donohoe said: "It just seems incredible that we live in a country that required women to leave their jobs and what we are living with now is the consequences of that.
"The advice I have available to me is that if we were to look to try to rectify this issue in one move in a single Budget, it would cost hundreds of millions of euro for me to do," he added.
"Over the next few years, we are going to try to move to a pension system, which takes into account the entirety of people's contributions. We're aiming to do that for around 2021." The Department of Social Protection said it estimated it would cost €60m next year to revert to the previous system. In 2012, the then government changed the eligibility criteria for the contributory State pension.
It moved to an "averaging rule" to calculate the number of contributions made by a worker.
Those entitled to a full pension were unaffected, but large numbers of those who would have been in line for smaller pensions lost out.
Under the old system, if you had an average of 20 contributions a year, you would be entitled to full State pension.
But the changes introduced in 2012 meant someone with 20 contributions a year got €35 less a week in pension.
Justin Moran, of Age Action, said that the failure to respond to the plight of tens of thousands of pensioners suffering because of the 2012 cuts was one of the biggest disappointments in the Budget.
"These changes have punished pensioners who took time out of the workforce to raise children and to care for their loved ones. Many have lost more than a €1,000 a year because of this.
"It's also important to remember that not every pensioner is going to get the €5 announced on Tuesday."
National Women's Council director Orla O'Connor said she was disappointed the issue was not addressed in this week's Budget.
Tuesday's Budget did very little for tens of thousands of pensioners who are losing as much as €1,500 a year for taking time out of the workforce to care for their families. They won't even get the €5 they read about in yesterday's paper.