After years of negotiations between EMI and Apple, the band's music became available on the music service last month.
McCartney told the Liverpool Echo: "I think people thought it was us holding it up, but that was just the record companies. We've always wanted it to go onto iTunes. If that's the way people are listening now, then that's great."
"That's the amazing thing about The Beatles' stuff. When we were in The Beatles we thought our popularity might last 10 years, if that. It lasted even longer than that, and now it's just gone mad. There's a whole new generation out there listening to those songs."
Comparing it to his listening habits while growing up, he added: "The other day I was trying to think what it must be like to be a teenager now who likes The Beatles. I suppose it's like me listening to Nat King Cole when I was a kid."