A standing-room-only crowed of about 2,700 attended Sunday's Mass at St. Patrick's Cathedral on Fifth Avenue.
Afterward, the 77-year-old Egan said he felt fine.
"I don't know what in the world happened to me last Saturday," he said. "I got this virus or something or other in my stomach and things weren't operating."
Egan was released from St. Vincent's Hospital on Tuesday. While he was there, doctors said he would need to have a pacemaker implanted.
"I've got plenty of time to do that," Egan said Sunday. "The heart is still ticking."
Egan is leaving after nine years leading the New York Archdiocese's 2.5 million Catholics in New York City and its northern suburbs. Milwaukee Archbishop Timothy Dolan will be installed as his successor on Wednesday.
Egan plans a busy retirement ministering to French-speaking Catholics at the new Sacred Hearts of Jesus and Mary mission on Manhattan's East Side.
"I am going to see if we can create a community that supports in a very special way what we call the Francophone community," he said.
During his homily, Egan spoke of a visit to China 35 years ago when a group of young people living under Mao's rule asked, "Tell us about God."
Egan said he told them about the resurrection of Christ, and when a young man asked if he believed it, he responded that "witnesses to the death and resurrection were not such as would invent such a story."
He said that Americans are fortunate to live in a country where religion can be practiced freely, though "the media are rather unfriendly."
He said the Easter message is more relevant than ever in the current gloomy economic time.
"In my 77 years I have never known a time when the proclaiming was as needed as it is now," he said.
Egan often has seemed a distant and aloof figure and has not cultivated a warm relationship with New York's media.
Asked about successor, he told reporters, "You're going to like him very much. He's going to talk to you much more than I do."
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