The pair had spent the day taking the plane down to Bodmin Airfield for an event to mark the 100th anniversary of the end of World War I.
It was as they were making their way back to Branscombe that the plane suddenly started to lose power, before the engine then cut out completely.
Rockey said: "We were flying along, taking in the view, when it began to lose power.
"It failed, the options available to me in the cockpit didn't work. So I had to look for somewhere to land.
"You look for somewhere near something or people so that if there are complications you will be able to get help more easily.
"You know what - I have had better runways. It was not ideal," he added.
Spiller said the incident had left her with "jelly legs" but said that she had complete faith in the "hero" pilot.
She said: "Zac is my hero. He is an amazing, fantastic pilot and I had every confidence in him, absolute faith that he would land it.
"As we came around the cliffs it began to slow up, then the next thing there was a total failure and the engine cut out.
"I turned around and called 'Zac' but of course you can't hear each other up there.
"He's looking out of the side of the plane and I started moving my arms telling people to get out of the way.
"I was slightly frightened. It wasn't like my life flashed before me or anything but I was thinking 'here we go'.
"I gave a sigh of relief as we landed and got out quickly but afterwards I have to admit I had jelly legs."
The aircraft was being dismantled by police and the coastguard, as there is no other way to remove it from the beach, and beach-goers were surprised to see the plane marooned on the coast.
Emma Salter, who lives nearby, visited the beach with her husband for an evening picnic to find crowds of people on the sand.
She said: "I asked one of the crew - there must have been around 15 of them - if the beach was closed, and he smiled and said no, but watch out for the plane.
"When we got down to the shore we couldn't believe what we were seeing - our friend, who volunteers for Sidmouth lifeboat, in his tractor towing a plane.
"I can only imagine how strange is must have been for people on the beach watching it land - you just wouldn't think it was going to land."
