West Ham last won the FA Cup in 1980 and finished runners-up in 2006.
"I need some poetry lessons to describe his (Payet's) importance to us. It is not just what he is doing with the ball. He is doing the dirty work too," Bilic told British media.
"Every week I want the questions about him to continue but it is hard to describe him. On the ball he is up there with Luka Modric from the players I have trained so far."
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Payet has scored nine goals in 25 appearances for West Ham in all competitions this season. The Frenchman joined the Hammers from Ligue 1 side Marseille in June last year.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)
