"The game on Tuesday showed the beauty of the game, what happened before was an ugly face. When I heard, I can't describe my emotions. It should never happen," Klopp, who wore an Irish tricolour liverbird badge in support of the victim, told reporters on Friday.
"It's unbelievable. All our thoughts and prayers are with Sean Cox and his family."
Liverpool beat Roma 5-2 at Anfield and will travel to Italy for Wednesday's return leg. The Merseyside club have requested a meeting with European soccer's governing body UEFA, Roma officials and Italian police to ensure the safety of their fans.
The German boss issued a plea for supporters to behave responsibly in Rome and focus solely on the football.
"It is only football. I never understood people who never understood that. I really hope people responsible for keeping people safe do the job well," Klopp added. "If Roma win that game and go to the final they will deserve it.
"Around the stadium no-one should think about anything other than the game.
"It is common sense. What can I say that they do not already know? Behave. Treat people how you want to be treated yourself."
Liverpool's immediate attention is on Saturday's Premier League game against relegation-threatened Stoke City.
Midfielder Alex Oxlade-Chamberlain will miss the rest of the season and the World Cup due to a knee injury while playmaker Sadio Mane also picked up a knock against Roma and is a doubt to play against Stoke.
"It's not fair but if you get a lemon you have to make lemonade out of it. We will wait for him like a good wife when the man is in prison," Klopp said when asked about Oxlade-Chamberlain's injury.
(Reporting by Aditi Prakash in Bengaluru; Editing by Toby Davis)
