The Hammers fought from a goal down to find themselves 2-1 ahead in injury-time before the Foxes were awarded a very late penalty when Andy Carroll clattered into Jeff Schlupp.
Leonardo Ulloa stepped up to convert from the spot to give Claudio Ranieri's side a share of the points but Bilic felt it was a poor call from referee Jon Moss who was under immense pressure throughout a dramatic clash at King Power Stadium.
"I'm not eagle-eyed, I'm not an ex-referee, I'm not Howard Webb, I'm a football coach and I don't want to talk about that," he said.
"On the contrary I would like to say it's hard for him. Not only here but here you have 32,000 people screaming at every contact in the box, every long ball in the box. If it's for the home side it's a penalty or handball.
"If it's in the other box it's cheat, dive or whatever. It's hard, it's extremely hard for him and the game went like crazy and they were losing and so it was extremely hard for him.
"It's easy now to say that the refs shouldn't get influenced by the fans. On paper it is easy to say that. Actually it's real life.
"Of course it's not a penalty."
Earlier, Jamie Vardy had put Leicester ahead with a fine finish in the 18th minute before he was sent off for a second bookable offence when simulating in the area prior to goals from Carroll (penalty) and Aaron Cresswell's superb volley.
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