The pair had originally planned to travel from Hawaii to Tahiti, but lost their boat's engine during damaging weather in May.
In a phone call with news media from the Ashland, Appel said they had sent a distress signal for 98 days with no response, according to the Honolulu Star-Advertiser.
They were found about 900 miles from the Japanese coast. They were adrift at sea with Appel's two dogs, Zeus and Valentine, cut off from the world.
"I'm telling you I've never seen any Stanley Cup victor come even close to the precision these five sharks had", Appel continued.
"I went downstairs with the boys and we basically laid huddled on the floor, and I told them not to bark because the sharks could hear us breathing", Appel said.
Although the Navy declared their boat, called the Sea Nymph, no longer seaworthy, Ms Appel said she hopes to eventually recover it and perhaps take it out again. "The two continued the calls daily, but they were not close enough to other vessels or shore stations to receive them", the US Navy said.
"They saved our lives", said Appel through the Navy release.More news: Plane carrying OKC Thunder dented by bird while landing at Midway
Asked if they ever thought they might not survive, she said they would not be human if they did not.
Miraculously, Fuiava and Appel were kept alive on a year's stock of dry goods, including oatmeal, rice and pasta. They were found thousands of miles off course after a series of troubles.
"The US Navy is postured to assist any distressed mariner of any nationality during any type of situation", said Cmdr.
Appel described the five months lost at sea as "very depressing" and "very hopeless". Steven Wasson, the commanding officer of the USS Ashland. They often had to get creative, such as when two of their watermakers (a device that turns salt water into drinking water) failed, and they combined working pieces from each of the machines to make a functioning one. The women will remain on board the USS Ashland until its next port of call.
"I'm grateful for their service to our country ... So she had several problems that caused her to end up drifting in the ocean", the elder Appel said. "The pride and smiles we had when we saw [the U.S. Navy] on the horizon was pure relief", said Appel.
"There's different sunrises and sunsets every day ... and you're around for a reason, but you may as well use the time to do something beneficial".
"Well, you gotta die sometime", Appel told ABC News."You may as well be doing something you enjoy when you're doing it".