No campaigners said they were considering a legal challenge to the outcome and called for equal funding for both sides for future votes.
Frances Fitzgerald, the children’s minister, said despite the low turnout, people would ultimately remember the change made to the Constitution.
There was still more work to be done on legislation and support services for children, she said.
“In relation to adoption, those young people who we talked about who are in a twilight zone and cannot be adopted because the bar is so high, it now means that those young people have a second opportunity at permanent family life.”
She said the passing of the amendment was an “historic day”, a comment echoed by Alan Shatter, the justice minister. He refused to speculate why 42% of voters had opposed the change.
Transport Minister Leo Varadkar said that the Government had to follow through on commitments now to protect children.
“This will include passing legislation to bring about equality in adoption law, enhancing child protection laws, the closure of St Patrick’s Institution, and the reform our family courts, among other measures.”
No advocate Richard Greene of the Christian Solidarity Party called for equal funding for both sides in future votes.
Writer and no campaigner John Waters said he felt there could be a legal challenge to the yes vote.
Barnardos chief executive Fergus Finlay said: “The Irish people have said they want to change the way we value and treat children in our society and in our laws.”