Chelsea were awarded a spot kick in the closing stages of their match against West Ham, after Ruben-Loftus Cheek went down under a challenge from Michail Antonio.
It appeared that the contact occurred outside the penalty area, but Robert Madley pointed to the spot.
Cesc Fabregas duly converted from 12 yards, to ensure that the match finished 2-2, and Bilic revealed that chairman David Gold was just as angry as he was with the decision.
“It was nowhere near the [penalty area] line,” the Croatian boss said. “It was obvious. It was easy because it wasn’t like he slid inside. It was way out of the line.
“It wasn’t the sort of game where I want to be moaning because I want to be talking about football, but this is the second week in a row.
“The Chairman emailed me a few days ago to say we have had four penalties in four years! That’s a record!”
West Ham had looked to be on their way to victory at Stamford Bridge, after goals from Manuel Lanzini and Andy Carroll put them into the lead.
However, Fabregas’ penalty ensured that the two sides could not be separated on the scoreboard.
West Ham have remained in contention to clam a Champions League qualification spot after the draw, but had they collected a win at Stamford Bridge they would now be occupying a top four position.