The ban means that Miller misses the games against Aston Villa, Reading and Manchester United.
It is the fourth time a Sunderland player has been sent-off this season. Paul McShane was sent off for a foul on Aleksandr Hleb, whilst Greg Halford was dismissed against both Luton Town (League Cup) and Fulham.
Roy Keane was far-from happy with the referee's decisions on Saturday. He had this to say about Liam Miller's sending off: "There's no doubt that once you raise your hand, there referee has no choice. I've been down that road myself before. I just felt that it could have been avoided.
"Clearly, you are not allowed to tackle the England captain because there was a big issue made of Liam's tackle on him, from himself and Pizarro. It was a foul but that was it.
"It was disappointing because it was a straight red and Liam will miss three games now. I think the referee could have maybe stepped in five seconds earlier because the reaction from Terry and Pizarro disappointed me. It was a foul but there was no nastiness to it."