Although the structure could barely be seen from the outside boundary, which is fenced and extensively planted in shrubs and trees, the flames were clearly visible from Sylvan Rd.
As well as admitting the arson charge, Motley pleaded guilty to one charge of wilful damage, and two of burglary, relating to the fire and an incident at a Hastings school.
Judge Pat Grace remanded the Hastings teenager on bail until his sentencing on June 12.
Arson is punishable by up to 14 years' imprisonment.
The wooden structure was built in 1977, 10 years after the opening of Fantasyland, which became Splash Planet.
It was closed to the public in recent times because it was deemed unsafe.
The ship was insured for $354,000.
Deputy Mayor Cynthia Bowers was pleased that Motley had taken responsibility and confessed to what she said was a "stupid act".
No decisions have yet been made relating to the nature of the replacement, which Splash Planet management hope to have in place for the 2016 season. The park is currently closed for the winter.
Ms Bowers said the pirate ship in its "heyday" brought a "huge amount of enjoyment to children around the region," including her own.
Ms Bowers had not given much thought to what could replace the popular ship.
"Rather than someone like me decide what it needs to be replaced with, we need to talk with our young people and see what they want."
The other two youths who were arrested in relation to the fire, aged 16 and 15, have appeared in the Youth Court.
At least one other person has been arrested in relation to suspected arson in the Mayfair-Parkvale area of Hastings, including incidents at St John's College and Karamu High School.
Karamu principal Martin O'Grady said the school had to take extra precautions when it became aware a series of suspicious fires had occurred.
