Supporters clashed and caused “chaos in the streets” of Southwark, south London, before the fourth round tie took place on 26 January.
A 27-year-old man was arrested on suspicion of wounding with intent, attempted grievous bodily harm and violent disorder, and was later bailed pending an appearance at a central London police station on 28 February.
Detective Sergeant Matt Simpson, from the Met’s public order investigation team, said: “The disorder which broke out on Saturday 26 January was some of the worst football violence we have witnessed for a very long time.
“It left one man with a life-changing injury to his face, and caused chaos in the streets.
“A post-incident investigation was launched, through which we are working hard to identify those involved in this completely unacceptable and shocking behaviour.
“We have today released images of 12 individuals we are attempting to trace in connection with this incident. The public can play a huge role in helping police, especially by assisting us in identifying wanted individuals. You are our eyes and ears.”
Scotland Yard previously said police experts had examined several hours of CCTV and hundreds of images related to the fighting.
The injured Everton supporter has posted a picture on social media showing a scar on the right side of his face.
Anyone with information can call police on 101 quoting CAD 5117 / 26 January, or contact Crimestoppers anonymously on 0800 555 111.