"I told him (Advocaat) I would like (him) to stay. You saw on the touchline he is a man full of energy and passion. The Premier League will be worse off without him," Croatian Bilic told West Ham's website.
"He is a man of knowledge, and his experience at different clubs in different countries and at international level is unbelievable."
The 68-year-old Advocaat took over from Uruguayan Gus Poyet in March and saved Sunderland from relegation last season and had initially intended to retire after their escape, but changed his mind and stayed on.
The manager had hinted strongly at his intentions on Saturday when he refused to confirm he was staying at the club after the West Ham game, from which the Hammers salvaged a point after coming from two goals down following Jeremain Lens' sending off.
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"It's his (Advocaat's) decision, only he knows what he feels. For a man of his experience, he's basically done everything in different countries, at international level," Bilic said.
"Only he knows but I rate him so much, there aren't many managers like him."
The decision to step down almost certainly spells retirement for Advocaat, who coached the Netherlands, Dutch side PSV Eindhoven, and Scottish side Rangers in a nomadic career, which also saw him become the first foreign coach to win the Russian Premier League title, a feat he achieved with Zenit St Petersburg in 2007.
(Reporting by Simon Jennings in Bengaluru; editing by Sudipto Ganguly)
