The comedian, 76, was diagnosed with the incurable disease in 2013 and announced his retirement from live performance five years later.
He told Chris Evans, on the Virgin Radio Breakfast with Sky, that he now walks "unsteadily" and his "hearing is going".
Sir Billy, known affectionately as the Big Yin, also rubbished the idea he had plans to return to the stage, saying: "It would affect my performance. I don't think the way I used to."
Across a six-decade career, Sir Billy was known for his energetic stage presence.
Symptoms of Parkinson's disease include decreased mobility and difficulty speaking, leaving him unable to perform as he did in his pomp.
He said: "I've stopped performing because of my Parkinson's disease and I've stopped touring.
"I may perform at some other point but I have no plans to. And I'm quite happy taking my medicine and getting along with it.
"I've started to drool which is a new one on me. This disease, it gives you a new thing every now and again that you have to deal with, and drooling is my latest.
"I walk unsteadily and my hearing is going and it's bizarre that bits of me are falling off but it's interesting."
"Give the guy a light in the tunnel."
Sir Billy is cared for by his second wife Pamela Stephenson, 69, with whom he shares three children. He has two other children from his previous marriage to Iris Pressagh.
He added: "It would affect my performance. I don't think the way I used to. I don't think at the same speed as I used to. And because I don't need to.
"I don't really know if the performance bit has gone because I have to get into the performance mode to see that. I'd have to walk on to the stage and I've never done that.
"And steadily more symptoms come and it's incurable. It's not going to end. As a matter of fact I had a Russian doctor in New York who said, 'You realise this is an incurable disease?'
"And I said: 'You got to get a grip of yourself, stop calling it an incurable disease, say we have yet to find the cure. Give the guy a light in the tunnel."
"Incurable is such an awful thing to say to somebody."
Sir Billy appeared in a BBC documentary about his illness in January, as he reflected on his life and career in showbusiness.