DUBLIN — The morning after Ireland learned it had become the first nation to approve same-sex marriage by popular vote, Diarmuid Martin, the archbishop of Dublin, looked out at the future of the Roman Catholic Church.

It could be found at St. Mary’s Pro-Cathedral here, in downtown Dublin, as two rows of children awaited confirmation before him in the lofty, column-lined church.

“Boys and girls, I made my confirmation 60 years ago,” he told them, adding, “Your world is different from mine.”

Not far away, the streets were quiet after a long night of celebrating. Revelers filled the bars, beeped horns, waved rainbow flags and drank Guinness after the result was announced on Saturday. The size of the victory energized supporters, with the referendum affirmed by 62 percent of the electorate and passed in all but one of Ireland’s 43 districts.