Jurgen Klopp told Liverpool fans going to Rome next week to avoid violence and not to seek revenge for the assault that left one of their own in a critical condition.
Sean Cox, a 53-year-old Irishman and father of three, is in a Liverpool hospital after suffering a serious head injury following an attack by Roma fans ahead of last Tuesday's Champions League semi-final first leg.
Two Italian men have been remanded in custody facing charges over the incident.
Liverpool won the game 5-2. The return is next Wednesday in Rome.
Liverpool are to hold talks with Roma, UEFA and the Italian police on Friday seeking reassurance over security.
At his press conference on Friday, Klopp wore a small pin of the club's Liverbird emblem in the green, white and orange of the Irish tricolour, as a sign of respect for Cox.
The Liverpool boss said his advice to fans going to Wednesday's second leg in Rome was to stay out of trouble.
"What can I say? Behave? It's easy to say!" said Klopp.
"Behave! It's common sense. You want to be safe. I never saw (trouble from fans) since I have been here.
"I really don't like that part of football. I don't get it.
"It should not be like this. It's a wonderful game and if we want away supporters at stadiums we have to show our responsibility."
The 50-year-old German - whose side play Premier League strugglers Stoke on Saturday - said Tuesday had been a day of mixed emotions.
"The game on Tuesday showed the beauty of the game, and showed the most ugly face of parts of the game," said Klopp.
"I heard first time about it, I cannot describe my emotions in English.
"That should never have happened and should never happen in the future."
Alex Oxlade-Chamberlain will be a major absentee for Klopp both on Saturday and for the Roma clash as he suffered a knee injury in Tuesday's match that will also ruled him out of the World Cup.
"We will wait for him like a good wife when her man is in prison," said Klopp.