The Glasgow-born comic described his initial forays into broadcasting work as “hellish” due to the level of resistance to allow a working class accent to be aired on network television.
However Sir Billy said he became “unstoppable” after overcoming prejudice about the way he spoke.
He also credited his accent with him becoming an overnight sensation in Scotland after a famous debut appearance on Michael Parkinson’s BBC chat show in 1975.
Sir Billy, 78, was speaking during an interview with his wife Pamela Stephenson for the Edinburgh TV Festival, which has just awarded the comic a lifetime achievement award.
Recalling his early TV career, which included appearances in the sketch show Not the Nine O’Clock News, Connolly said: “It was hellish. They never stopped. I had to eventually say to people: ‘This isn’t a speech impediment, it’s an accent. Treat me right and leave my material alone, it will work.’
"I had to convince them that it would work. Eventually I got through and it worked and it was lovely.
“It’s funny with the accent. When an Englishman gets famous he just speaks like an Englishman and can be from Yorkshire, Cornwall or Liverpool. People don’t bother.
"But when I open my mouth people go ‘oh, Scotland.’ You’re stamped Scottish."
Discussing his relationship with Scotland and the impact his Scottish roots had had on his career, Sir Billy said: "First of all there is the accent. It is a working class accent. There's a lot of battles to be fought in Scotland with that. They didn’t like working class accents in broadcasting. Now they’re all over the place. It’s brilliant. That was the main hurdle. Having conquered that, I was unstoppable.
"The other thing was that I had no regard for that pseudo-folk stuff that the kilty guys all sing about Scotland.
"I hated that from when I was a child, so I used to take great delight in stamping all over it. It’s worked out great. Scotland is such an identifiable mark.”
Sir Billy was famously given a hero’s reception in Glasgow Airport after his debut appearance on Parkinson’s prime-time show.
He recalled: “It was kind of weird. I’d never known anything like it or done anything remotely like it.
“It’s a thing the Scots have got about accents. You can be as popular you like, but if you don’t have a Scottish accent it it’s different.
"They loved the fact that I went on with my Scottish accent and got famous. They took it personally and all applauded.”
The comedian, who was diagnosed with Parkinson’s disease in 2013 and retired from live performances five years later, also said the medical challenges he faces while filming for television are “getting worse”.
He said: “The challenges lately have been medical. They are getting worse. I will have to weigh it up and see how bad it gets. Play it by ear.”