Commander Richard Farrington said the crew of HMS Nottingham responded rapidly to the accident as water gushed aboard.
"It felt like a series of very heavy judders. I knew that we had collided with something," he said.
"I prayed to God it was a container, or even God forbid a small boat or something. I had no idea it would be the world's biggest rock.
"It is the worst feeling in the world.
"We have done some significant damage to a major British warship. This is not a good day for me."
The accident on Sunday happened in poor weather near Lord Howe Island, 300 miles north-east of Sydney in the Tasman Sea.
The 3,500-tonne ship is now at anchor while divers assess the damage and water is pumped out with the help of equipment provided by the Australian Defence Force.
Risk of sinking
The commander, who has been in charge of the ship for 18 months, said water began gushing into the ship and the swell beneath it created urgent problems.
"I remember running up to the bridge and there was white water on both sides, probably about 30 metres back from the bow and the ship was sitting up and dropping down on to the rock with a swell, there was a big swell."
The commander said his crew of 253 faced the difficulty of securing the vessel off the rock, but facing a high risk of sinking.
The surge of water under the ship made remaining atop the rocks impossible.
"At the right moment [we] came hard of stern, off she came without too much problem," he said.
But he added: "It was an interesting call as to whether to sit on the rock and know that we would not sink, or get off it and run the risk of sinking.
"My view is that if I had stayed on the rock she would have broken her back very quickly because the swell was big."
The vessel was on a routine trip from Cairns, in Queensland, north-east Australia, to Wellington, in New Zealand.
Commander David Heley, from the MoD said the vessel was in "good hands" with Commander Farrington.
"He is a cool, phlegmatic individual," he said.
"Obviously, this will be a major challenge but I have every reason to suspect he'll handle this incident with great professionalism."