He recalled, during the ceremony, his first failed songwriting attempt with former Faces band mate Ronnie Wood.
He added Wood's mother had said: "I don't think the Beatles have got anything to worry about."
Stewart went on to write a number of hits, including Do Ya Think I'm Sexy, You're in my Heart and Young Turks.
Although the seven albums he has released since 2001 have just featured covers of other people's songs, the singer said the ASCAP honour would "maybe give me a push up the bum to start writing again".
The 66-year-old is currently working on a blues album with Jeff Beck, covering such tunes as Muddy Waters' Rollin' and Tumblin.
Also at the ceremony, two of the year's most prolific hit makers, Lukasz "Dr Luke" Gottwald and Max Martin, were named songwriters of the year.
The duo penned five of the most performed songs of 2010 together, including Katy Perry's California Gurls and Teenage Dream, as well as Taio Cruz's Dynamite.
It is the fourth time Swedish songwriter-producer Martin - who has had 20 number one songs in the past five years - has received the honour.
Train front man Pat Monahan won song of the year for Hey, Soul Sister, while EMI Music Publishing was named publisher of the year.
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