The England international, who had been substituted during the second half, had to be escorted down the tunnel following the incident, but what sparked the incident remains unclear.
Baggies boss Alan Pardew admitted he saw Livermore, 28, in among the crowd at the London Stadium but did not know what had happened to prompt his actions.
Pardew, who will look into the incident, said: "The only thing I know is I see Jake in the crowd, which disturbed me. Obviously you don't want to see a player in the crowd.
"There's no way he's going in the crowd - because I know him, he's a great lad - unless he was provoked severely. That's all I know.
"I haven't had a chance to talk to Jake. I'll speak to Jake and we'll go from there."
West Ham manager David Moyes claimed he did not see the incident, but added: "I didn't know about it, but I've been told something happened."