It is not the first time a high profile footballer has suffered vile abuse on Twitter and other websites after a mistake.
"I am probably going over the ground I did with Tammy before," Lampard said after the game to reporters.
"Firstly it is a person that does it, wherever they are hiding from, and secondly we have to look at social media and the platforms and give them some accountability to actually have people register who can be chased down for it.
"I think it is simple, until we get to that, and no matter how horrible that conversation is, we get tired talking about it.
"Until there is some culpability, anyone can say anything to anyone. It's not just racism, it could be calling them names, homophobia, sexism, it could be anything.
"If we allow it, then unfortunately in modern society it is out there and it has to be dealt with."