In an interview to mark his 90th birthday, the Duke said he felt "sad" the vessel, which is now permanently moored at Leith docks, had been taken out of service.
He told broadcaster Alan Titchmarsh that the royal yacht was "sound as a bell" and could have sailed for at least another five decades if her steam turbines had been replaced with diesel engines.
HMY Britannia, which attracts about 250,000 visitors every year, has been based at the historic Edinburgh port since the city won the right to moor her in 1998.
It was bought by dock operator Forth Ports for just 250,000 and has operated as a visitor attraction and corporate hospitality venue ever since.
Money raised by visits and tours goes into a maintenance fund held by The Royal Britannia Trust charity.
However, the five-star attraction has also generated hundreds of thousands worth of business for Edinburgh restaurants, hotels and attractions surrounding its location next to Ocean Terminal.
In the documentary, due to be aired tomorrow night, Prince Philip reveals that his interest in design led to an early involvement in Britannia, which was both an ambassador for Britain and the Royal Family's home from home.
He expressed his regret that the government made the decision to decommission HMY Britannia after just 43 years. When asked what should have happened, he said: "She should have had her steam turbines taken out and diesel engines put in.
"She was as sound as a bell, and she could have gone on for another 50 years."
A spokeswoman for Visit Scotland said: "The decision to decommission The Royal Yacht Britannia was taken by the then UK government.
"Since it opened as a visitor attraction, however, Britannia has been a very popular part of the tourism offering in Edinburgh and Scotland, attracting visitors from all over the world. Last year almost a quarter of a million people visited the five-star Royal Yacht Britannia and it has consistently been one of the top 20 paid-for visitor attractions in Scotland since it opened."
For the first time since it arrived in Leith 13 years ago, the yacht is preparing to undergo a 100,000 make-over. It be closed for at least a month from January 2012 to allow its vast hull to be fully inspected, treated and repainted.
Marine inspectors will oversee the revamp of the area below the waterline after the yacht's insurance company insisted it needed a "clean bill of health".
Background: Royal tour to sign off service
FOR more than four decades, the Royal Yacht Britannia carried the Queen and the Royal Family around the world on 968 official voyages.
Launched in April 1953 at John Brown's Clydebank Shipyard, it travelled 1,087,623 nautical miles and called at more than 600 ports in 135 countries.
Its crew consisted of 220 Yachtsmen, 21 Officers, and three Season Officers and a Royal Marine Band of 26 on royal tours.
In January 1997, Britannia set sail from Portsmouth to Hong Kong on its last and longest voyage.
On 11 December that year it was decommissioned at Portsmouth Naval Base in the presence of the Queen, the Duke of Edinburgh and 12 senior members of the Royal Family.
Four months later, after intense competition from cities around the UK, Edinburgh was chosen as the yacht's new home.