Accepting the special trophy at the Q Awards, Ono said Lennon had sometimes felt insecure about his songs, asking why "they always cover Paul's songs and never mine."
"I said, `You're a good songwriter, it's not June with Spoon that you write. You're a good singer, and most musicians are probably a little bit nervous about covering your songs,'" she said Monday.
McCartney has sometimes clashed with Ono, Lennon's widow.
She objected when McCartney reversed the traditional "Lennon-McCartney" songwriting credit on his 2002 album, "Back in the U.S." Ono's spokesman accused him of attempting to "rewrite history."
McCartney had earlier complained that Ono wouldn't let him take credit for "Yesterday," a song written entirely by McCartney.
Oasis took the best album trophy and the people's choice prize at the awards, sponsored by British music magazine Q. Coldplay was named best act in the world.