Pirlo, now at Major League Soccer outfit New York City FC, is one of the greatest players in football history.
The Italy international midfielder has won the Champions League twice and the World Cup once among other major honours.
Bilic, who rates Pirlo highly, believes that West Ham attacking midfielder Payet is similar to the 36-year-old.
“They tried to mark Andrea Pirlo for three years,” the Hammers boss has written in The London Evening Standard. “He plays in a central position so he is always in front of you and you think it is easy to mark him with two or even three players.
“I am sure every manager when they played against Juventus was saying: ‘Mark Pirlo.’ Yet still Pirlo was always unmarked and after the game the coaches would ask: ‘Why didn’t you mark him?’
“The answer is that it is about Pirlo — and now for us, it is about Payet. Also the rest of the team help him. In the second half against Villa, Mark Noble was excellent, as was Alex Song and Cheikhou Kouyate and they can also benefit from the opposition trying to mark Payet.”
Payet has been one of the best players in the Premier League so far this season, having joined West Ham from Marseille in the summer of 2015.
The 28-year-old attacking midfielder has scored six goals and created 61 chances in 17 league appearances for the Hammers so far this season.
The France international has a pass accuracy of 82% and a shot accuracy of 70%, and has won one header, 45 headers and 11 tackles.
West Ham are sixth in the Premier League table at the moment with 39 points from 24 matches, six points behind fourth-placed Arsenal.