Mandy Rodford, 45, and her husband John, 46, were celebrating their fourth wedding anniversary on the vessel when it ran aground off an Italian island on Friday.
The couple, from Rochester in Kent, had only been on board the Mediterranean cruise ship for seven hours before disaster struck.
Mrs Rodford, who had been hesitant about going on the holiday because she does not like water, said: "I just thought my life was gone. I just thought my life was over, getting in that water.
"I thought, if I don't die from the swimming part, I'm going to die from the shock of having to get in it."
Speaking at Heathrow airport after flying back from Rome, Mr Rodford explained how they first thought something was wrong when they were eating their dinner.
He said he heard "a crunch", then his drink started sliding along the table.
The couple asked a crew member if there was a problem, but they were told: "No, it's the engine."
He said: "Then the lights went out and came back on. And then it (the ship) started going the other way, and quite a lot the other way. All the plates were coming off the tables and smashing, and it was just like bedlam.
"Everyone was getting the life jackets, but they told us to stay. They said: 'It's all right, it's under control'."
The couple explained how they first went to the side of the boat the furthest from the water to escape but because the ship had listed at such an angle, the lifeboats could not be winched down.
Mr Rodford said: "We all got in them, and we got so far down, but we had to get back out of them."
His wife added: "They were hitting the side of the boat. Normally they are hanging and they would release them down.
"But because the boat was like this (at an angle), as they were releasing the lifeboats they were hitting the side so they were stuck. I couldn't believe it."
The couple had chosen a cabin on the sixth floor without a window, because of Mrs Radford's fear of water, and their room was on the side of the ship submerged in the sea.
Mr Rodford joked: "The little mermaid's got all my belongings. The lot!"
Asked if they would consider taking another cruise in the future, Mr Rodford said: "I'm not going on a cruise again."
His wife added: "Never, ever, ever."