The 70-year-old musician - who replaced former drummer Pete Best two years after the original line-up was formed - claimed he was better known in Liverpool than The Beatles when he joined, and they were fortunate he chose to work with them.
He told Live magazine: "Within Liverpool, I was a lot more well know than them. Rory and the Hurricanes (Starr's former band) were big shots in the city. We had the suits. That was our claim to fame. The Beatles were lucky to get me. It wasn't just that I was a big shot; I was a cool drummer."
Ringo is currently touring with his own group Ringo Starr and his All Starr Band, and revealed that his former band mate Sir Paul McCartney says he is too busy to work with Ringo whenever the drummer asks him.
He continued: "Every time I ask him to tour with the All Starrs, he says he is too busy. We're as close as we want to be. We're the only two remaining Beatles, although he likes to think he's the only one. I actually think it's people on the outside who perceive Paul as thinking he's the only member left, when actually it's me. I am the last remaining Beatle