A man was stabbed and violent battles broke out between rival fans outside Upton Park in what police labelled "large-scale" trouble.
When the match did get under way it was marred by several late pitch invasions as West Ham went on to win in extra-time.
Hundreds of fans were involved in the disorder which police said was caused by people without tickets to the second-round tie who had planned to start trouble.
Police said later that the victim of the stabbing was a 44-year-old man who was in a stable condition in hospital.
A Football Association spokesperson said: "We absolutely condemn all of the disorder that has occurred at Upton Park this evening both inside and outside of the ground.
"We will be working with all parties, including the police and clubs, to establish the facts surrounding tonight's events.
"We strongly expect all culprits to be banned from football for life. They have no place in our game."