Bilic was dismissed by referee Mike Dean after remonstrating with the official on the pitch at half-time.
The Croat, who has been charged with improper conduct, could now face a two-match touchline ban if evidence of abusive or insulting language is found.
An FA spokesperson said: "It is alleged that the West Bromwich Albion FC manager's language and/or behaviour on the field of play at half-time of the Premier League fixture against Everton FC on 19 September amounts to improper conduct."
Bilic, who has until Thursday to respond to the charge, claimed he had approached Dean seeking an explanation as to why Dominic Calvert-Lewin's first goal for Everton was awarded by the video assistant referee, having initially been ruled out.
He said: "As a manager I should be in a situation to ask the referee what's going on.
"It's not like the game was going on, it was half-time - nobody was around. I didn't swear. I asked him in a frustrated way but I didn't go over the line. But he just ignored me and gave me red.
"As a manager you have that right if you are not crossing the line. I told him if you want to kill us, kill us. That's all."
Bilic was sent-off just moments after Albion left-back Kieran Gibbs was red carded for an off-the-ball shove on Everton’s James Rodriguez.