Some believers expressed bewilderment or said it was a test from God of their faith, after the day passed without event.
Meanwhile, the evangelist at the centre of the claim, Harold Camping, has not been seen since before the deadline.
He had predicted that Jesus Christ would return to earth on Saturday.
True believers would then be swept up, or "raptured", to heaven, he had pronounced.
The 89-year-old has used broadcasts on a Christian network and billboards to publicise his ideas as part of a campaign that went global.
He said biblical texts indicated that a giant earthquake on Saturday - which he said would begin at 1800 at various time zones around the world - would mark the start of the world's destruction, and that by 21 October all non-believers will be dead.
Robert Fitzpatrick, a retired transportation agency worker in New York, said he had spent more than $140,000 (£86,000) of his savings on advertisements in the run-up to 21 May to publicise the prediction.
After 1800 passed and nothing had happened, he said: "I do not understand why... I do not understand why nothing has happened."
"I can't tell you what I feel right now. Obviously, I haven't understood it correctly because we're still here." (read more)