The Archbishop of Dublin says the rights of gay and lesbian people could have been legally recognised without changing the definition of marriage.
Diarmuid Martin says the council of bishops will meet tomorrow to discuss the outcome of the referendum.
He says there is currently no engagement between modern Irish culture and the Catholic Church here.
Speaking at the Pro Cathedral in Dublin, Archbishop Martin explained he believes in an equality which recognises difference:
Meanwhile, in the wake of Ireland’s historic vote to approve same-sex marriage, the Australian prime minister has rejected calls for a referendum on the subject.
Prime Minister Tony Abbott said the federal parliament would deal with any changes to the law that were brought before it, and that referendums were reserved for constitutional changes.
Mr Abbott is a long-standing opponent of same-sex marriage, but his latest stance has provoked criticism on social media and from politicians.
Opposition leader Bill Shorten, speaking to ABC, said "most places in the world are dealing with marriage equality, why is Tony Abbott stopping Australia becoming a more modern nation?"