Television replays showed the Dutchman was not the player who had pushed Teddy Sheringham in the face but Halsey sent off the Blues striker.
It appeared to be team-mate Mario Melchiot who shoved Sheringham in the face.
An FA spokesman said: "We're waiting for the referee's report before we do anything."
Chelsea boss Claudio Ranieri admitted Hasselbaink's dismissal had probably not turned the course of the game, although, he said "it was very difficult for us without our target man".
Ranieri added: "Just when the spirit of Chelsea wanted to try to change the result, Jimmy was sent off. It was unbelievable.
"He told the referee that he hadn't done anything. Sheringham also told the referee that it was not Jimmy but Melchiot instead, while Melchiot said it was him as well. But Jimmy was still sent off."
Sheringham told ITV: "I didn't see what happened, all I know was someone pushed my face. I said to the ref 'I don't know who it is but he doesn't deserve to be sent off'."