Ireland was the first country in the world to put same-sex marriage to a popular vote and the May 22 poll was backed by 62 per cent of the population. Same-sex marriage is now a constitutional right in Ireland.
"I think really that the Church needs to do a reality check, a reality check right across the board, to look at the things it's doing well, to look at the areas where we really have to start and say, 'Look, have we drifted away completely from young people?' ” Martin told state broadcaster RTE as the result became clear.
He said the referendum result was "an overwhelming vote in one direction," and he appreciated how gay men and lesbians felt after the endorsement of same-sex marriage — "that they feel this is something which is enriching the way they live," he said.
The archbishop described the result as a "social revolution."
"It's a social revolution that didn't begin today," he said. "It's a social revolution that's been going on, and perhaps in the Church people have not been as clear in understanding what that involved.
"It's very clear that if this referendum is an affirmation of the views of young people, then the Church has a huge task in front of it to find the language to be able to talk to and to get its message across to young people, not just on this issue, but in general."
Martin said it was important that the Church must not move into denial of the realities.
"We won't begin again with a sense of renewal by simply denying," he said.
Referring to the high turnout of younger voters, the archbishop said "most of these young people who voted 'yes' are products of our Catholic schools for 12 years ... there's a big challenge there to see how we get across the message of the Church... We need to sit down and say 'Are we reaching out at all to young people?'... We're becoming a Church of the like-minded, and a sort of safe space for the like-minded," he warned.
However, he insisted, "that doesn't mean that we renounce our teaching on fundamental values on marriage and the family. Nor does it mean that we dig into the trenches."
"We need to find ... a new language which is fundamentally ours, that speaks to, is understood and becomes appreciated by others," the archbishop said.
Bishop Kevin Doran of Elphin, who had been a leading voice in the "no" campaign, described the outcome as "clear and decisive."
"It seems that many people voted 'yes' as a way of showing their acceptance and their love for friends and family members who are gay," said Doran. "Large numbers obviously believed that they could vote 'yes' without in any way undermining marriage. While I do not share their belief, I understand their reason for celebrating, and I do respect their spirit of solidarity."
Turnout was significantly higher than previous referendums, and most commentators highlight the large number of young voters as a key reason why the referendum passed.
The government plans to have legislation prepared by this summer, with the first same-sex marriages expected to take place in September.