Anti-abortion campaigners have described the decision of Irish voters as a "tragedy of historic proportions".
The Save the 8th campaign, which conceded defeat on Saturday morning, said a wrong did not become a right simply because the majority supported it.
Communications director John McGuirk said the unborn child no longer had a right to life recognised by the Irish state.
"Shortly, legislation will be introduced that will allow babies to be killed in our country," Mr McGuirk said.
"We will oppose that legislation," he said.
"If and when abortion clinics are opened in Ireland, because of the inability of the government to keep their promise about a GP-led service, we will oppose that as well.
"Every time an unborn child has his or her life ended in Ireland, we will oppose that, and make our voices known."
Anti-abortion campaigner Cora Sherlock said she was saddened by the results.
"A lot of misleading claims were made about Ireland's healthcare," she said.
"I'm very upset that women were made to feel like they should be frightened going into Irish hospitals, which was a failing of Yes campaigners because our international record is fantastic in this area."
Independent TD Mattie McGrath, who advocated for a No vote, said the support for repeal was not evident to him on the doorsteps during the campaign.
"The people have spoken and I accept the will of the people," he said.
Mr McGrath told RTE's Referendum 2018 programme that he would hold the Taoiseach and health minister to their words that abortion would be rare and restrictive.
He added that he hoped the concerns of the No voters would be taken into account in the legislation.
Independent senator Ronan Mullen, who drew criticism for his views on abortion and mental health during the campaign, said he had a strong sense of sadness about the voters' decision.
"A lot of unborn children will lose their lives in the future, that's what happens when abortion gets legalised," Mr Mullen said.
"I'd asked people to keep those children in their thoughts and prayers today, and their mothers and those involved in taking their lives."
The senator said he would not be supporting legislation that came through parliament.
He claimed that when abortion was available as a matter of choice, children with disabilities would suffer.
The government's proposed legislation does not permit abortion on the grounds of pregnancies with diagnosis of disability.
Prominent anti-abortion activist Declan Ganley tweeted when the first exit poll results emerged on Friday night.
It read: "When due to the snuffing out of their human rights, the first of countless thousands of Ireland's unborn children are killed in Irish clinics or hospitals, all those that voted No can at least know you fought the good fight to try to save those little ones. Heros [sic] all."
Read more:
- What happens now the Republic of Ireland has repealed the eighth amendment?
- Pressure mounts for law change in Northern Ireland
