The Northern Ireland Assembly held the debate after Sinn Fein brought a motion calling for a new law on marriage equality.
Earlier the country's Health Minister, DUP politician Jim Wells, resigned following controversial comments he made last week about same-sex relationships where he suggested children brought up by gay parents were more likely to be abused.
CARE in Northern Ireland Policy Officer Mark Baillie said: "Marriage is the union between one man and one woman.
"For the good of society it is vital this traditional view of marriage is upheld and so CARE warmly welcomes the fact a majority of MLA rejected this latest move to redefine marriage.
"Just because the rest of the United Kingdom have introduced same-sex marriage does not automatically mean we should do the same in Northern Ireland.
"After four attempts to redefine marriage in this Assembly, it seems only right that this issue should not be considered again within the mandate of this Assembly.
"This Assembly's view on this question is now very clear, and Northern Ireland faces many other pressing issues going forward."
DUP Assembly member Peter Weir said: "This is not a serious debate. Clearly this motion is an attack on the symbolism of marriage and the institution of marriage and an attempt to redefine marriage.
"My party believes, and I believe also, that marriage is between one man and one woman and once you redefine that you lose the essence of marriage itself."
But the SDLP's Colm Eastwood said: "We need to be seen to be embracing all members of our community.
"There is no reason why the north of Ireland should be the only place on these islands that doesn't have marriage available to same sex couples."