The 28-year-old Argentine, who can play as a forward or as an attacking midfielder, was on target for the Hammers against West Brom at the Boleyn Ground in the Premier League clash.
The former Lazio star scored with a wonderful free kick from 25 yards, but Bilic was not surprised with the feat.
“Mauro has got it and it is a natural talent he has got with the way he shoots the ball,” the West Ham boss told the club’s official website. “Whether it is from free-kicks or open play when he scored against Chelsea.
“He practices that every day in training and it wasn't a surprise to see him do that. It was a great goal.”
Zarate was substituted in the 82nd minute, as the Premier League encounter ended in a 1-1 draw.
The Argentine took six shots, had a pass accuracy of 81%, created one chance, put in five chances, attempted four dribbles, won 83% of his tackles, and made one block.
So far this season, Zarate has scored three goals and created eight chances in 10 Premier League appearances.
The West Ham attacker has a pass accuracy of 86% and a shot accuracy of 60%, and has won one header, 12 dribbles and 17 tackles.