The group went their separate ways in 1970 after the singer - who was shot dead in 1980 - decided to quit but his former bandmate insisted he, Ringo Starr and the late George Harrison never considered continuing as a three-piece because they felt so ''fed up''.
Speaking to Howard Stern on SiriusXM, Paul said: ''It's like a family, when families break up it's to do with the emotion and the emotional pain, you can't think of a smart idea like that at the time, you're hurting too much, it wasn't going to happen.
''We'd been through too much and I think we were just fed up of the whole thing.''
When the DJ discussed the songwriting partnership Paul and George could have enjoyed, the 77-year-old superstar admitted the 'My Sweet Lord' hitmaker's writing abilities had often been underestimated because he was a ''late bloomer'' when it came to penning lyrics.
Paul said: ''I take your point, it was easy to underestimate George because me and John had always written most of the stuff and most of the singles.
''George was a late bloomer as far as writing was concerned, he wasn't that interested in the beginning and then he stared to get interested and boy, did he bloom. He wrote some of the greatest songs ever.''
The 'Live and Let Die' singer is a big fan of the Rolling Stones - whose current line-up comprises Sir Mick Jagger, Keith Richards, Charlie Watts and Ronnie Wood - but admitted he still thinks his own group were better.
He said: ''The Stones are a fantastic group, I go and see them every time they come out because they're a great band and Mick can really do it, the singing and the moves and everything, Keith, Ronnie, and Charlie, they're great, I love them.
''Their stuff is rooted in the blues, when they're writing stuff it's to do with the blues, whereas we had a little more influences.
''Keith once said, 'You're lucky man you have four singers in your band, we've got one'. I love the Stones but I'm with you, the Beatles were better.''
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