Eleven Liverpool fans have been stabbed before or during the Uefa Cup match against Roma.
Six British fans were taken to Rome hospitals, and two Norwegian Liverpool fans were also stabbed.
Three English supporters were also stabbed in the early hours of Thursday following isolated attacks in the city centre.
The Foreign Office said none of their wounds are thought to be life-threatening.
Superintendent Dave Lewis of Merseyside police, who was liaising with Italian officials at the match, said Liverpool fans had been well behaved.
And he blamed the violence on Italians targeting small groups of away supporters.
He said: "We believe the victims were in the vicinity of the stadium when they were attacked.
"There is the possibility that these people travelled by taxi and then were attacked as they made their way around the stadium.
"There were no large confrontations between rival fans. These were again separate incidents where home supporters appear to have targeted either individuals or small groups."