"There was a bump and a scraping noise but I wasn't worried at first," said Mrs Donoff (formerly Janice Cowan), 59. "I've been on cruises before and these things don't happen."
Told over the Tannoy that the generator had failed, Mrs Donoff said she became concerned because the ship had come to a halt.
"We decided something was amiss and that we should dress warmly," said Mr Donoff, 62, the chairman of the Jewish Children's Holiday Fund. "We saw people were wearing life-jackets, so we took our passports and I stuffed my siddur and tefilin into my pocket."
With the ship listing at an 80-degree angle, their walkway became the walls of the ship.
It was not until 4.30am that they finally escaped by scrambling up a ladder to one of the ship's portholes, then using a rope to clamber down and drop on to the coastguard's boat.
"It was chaos," said Mrs Donoff. "We knew if the ship went down while we were inside, we wouldn't get out."
The evacuation took hours as hundreds of the ship's 4,000 passengers and crew were using the same route. "People were pushing and shoving. They were terrified." During the chaos Mrs Donoff lost her shoes and life-jacket. "I looked at the ladder and I thought 'I can't do this'."
"If you slipped, then you would have fallen five floors down to a certain death," added Mr Donoff. "It was very emotional - everyone was praying.When I was going down the ladder my tefilin fell out, but I managed to pick them up."
After they reached land, the Donoffs called their children, who live in Britain, Israel and New York. "They wouldn't normally answer the phone on Shabbat, but I left messages," said Mrs Donoff. "We didn't want them to go to shul and hear, we had to tell them we were OK."
They were critical of Costa Cruises for the lack of help to return home. "There was no information about what was happening - we didn't know that there were still people on the ship," she said.
Costa is a subsidiary of the American-Israeli company, Carnival Corporation & plc. Its Israeli-born chief executive, Micky Arison, said on Twitter that his thoughts and prayers were with the passengers and crew.
The Donoffs flew home on Sunday and have been inundated with messages from friends all over the world.
With some understatement, Mrs Donoff said drily: "It was not quite the honeymoon we were expecting.
"But somebody this week asked why we were so upbeat. I said we were just so happy to be alive. On more than one occasion, we thought we wouldn't get through this. When you get married later in life you don't know how long you'll have together. But we didn't think we'd only have 11 days."
