Bilic wished to focus on the fine performance of his team and was frustrated at facing questions about the "unacceptable" behaviour of a minority.
"I noticed it, of course," Bilic said. "The game was on. I was more concentrated (on the game). I don't know what happened. But whatever happened, we are totally against it as a club as a team.
"For those kind of things to happen, especially in England, is unacceptable."
Bilic was unhappy to have to address the violent scenes in his post-match media conference.
"Straight away, (for) the second question to be about something that I have nothing to say about is unfair towards the game," he said.
"I think this game deserves to be talked about a little bit more.
"Ask me one question about the game. It was a London derby, 2-1 for us. Some great performances."
There had already been disturbances in the stands and outside the ground at some of West Ham's previous home matches, and a series of measures were put in place ahead of a first London derby.
The clubs appealed to supporters for the tie to pass peacefully, but the entertaining match was overshadowed.
West Ham were well in control of the tie at that point. Cheikhou Kouyate rose ahead of restored Chelsea captain John Terry to head the Hammers in front and Edimilson Fernandes struck a second three minutes after the interval with Gary Cahill scoring a late consolation.
The Hammers boss had already spoken of a "great night for us", but the repercussions could be significant with the authorities sure to scrutinise the scenes.
Bilic added: "It's a great night for us. To put that kind of performance from us is really very important for us, not only for this competition but in general to gain more confidence in the team, individual and even more as a team.
Chelsea head coach Antonio Conte had on Tuesday spoken positively of the atmosphere in English football and had hoped for the game to pass peacefully.
Conte, who was focused on the on-field action, said: "I didn't see the situation. We were playing and I didn't see this. I don't like this type of situation. It's important to see the right atmosphere.
"Above all in England, we are used to see the right atmosphere. This country is fantastic.
"I'm sorry about this situation."
West Ham: Randolph, Kouyate, Reid, Ogbonna, Fernandes (Feghouli 66), Noble, Obiang, Cresswell, Antonio (Zaza 82), Payet, Lanzini (Ayew 78).
Subs Not Used: Nordtveit, Adrian, Collins, Fletcher.
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