In a remarkable match at Goodison Park, the Baggies put in an excellent first-half performance that saw them take the lead after 10 minutes through Grady Diangana.
Everton levelled just after the half-hour mark through Dominic Calvert-Lewin with a goal stepped in controversy.
The striker, who was stood in an offside position, back-heeled in following a Richarlison header.
Initially ruled out for offside, VAR showed Richarlison's header took a slight deflection off Darnell Furlong and was then given.
But the game then turned chaotic just before half-time following a stunning strike from James Rodriguez to put the hosts ahead.
The Colombian then collided into Kieran Gibbs who was then sent off for shoving the former Real Madrid man in the face.
Bilic was also sent off for arguing with referee Mike Dean at half-time.
Albion then conceded three poor goals in the second half to fall to defeat.
“We did so many mistakes we can’t do at this level," Bilic said.
“Why I’m frustrated is the way we were tactically in the first half, we were closing them down, passing the ball, the way we pressed them, it can’t be 2-1 for them.
"To show that naivety to go down after we are 1-0 up and to get the red card is frustrating.”
On the Gibbs red card, Bilic said: “He can’t do that, he’s old enough.
"He’s experienced. He played a great game until then. He reacted to something James did to him but he wasn’t clever enough to go down when he clipped him. He reacted and gave the referee no choice.
"It was our mistake.”
Asked about his own red card, the boss said:: “The analysis guys told me it was a foul for us before their first goal.
"They should have seen that Dominic Calvert-Lewin is going for the ball and doesn’t touch it. The reason Darnell Furlong is heading towards goal, it’s a foul.
"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."
Ultimately, though, Bilic admitted his team's defending in the second half wasn't good enough.
“We showed some naivety," he added.
"We had enough players to defend the set-plays. We saw everything in this game – a lot of quality, a lot of things to be proud of and build on. Just copy and paste in next game.
"But unfortunately there are enough things we can’t do on this level.
“We have only ourselves to blame. There shouldn’t be lessons. We have set-plays in the Championship against some teams even more dangerous than this level.
"The amount of 6ft whatever guys. You can’t switch off.”