A couple I've heard (though I'm not sure these would qualify as put-downs) credited to Jascha Heifetz:

After a concert a woman said to him "Your Guarneri never sounded so beautiful" and Heifetz then held the violin to his ear and said "Funny, I don't hear anything?"

An admirerer said to him "I'd give anything to play like you" to which he responded "Would you give 16 hours a day for your entire life?"