Liverpool won 5-2 when the teams met at Anfield on Tuesday, though the result was overshadowed by an incident outside the ground prior to kick-off.
Two men from the Italian capital have been charged in connection with an attack on a 53-year-old man, who suffered serious head injuries and remains in a critical condition.
Representatives from both clubs, UEFA, local police and security services will meet to discuss fan safety prior to the return fixture, with Klopp hoping the two sets of supporters respect each other at the Stadio Olimpico.
"It's only football. I never understood people that don't get that," said the German.
"I really ask for responsibility, from everyone. If Roma win that game and go to the final, then they deserve it. If we win and go through, we will deserve it. That's the competition.
"We expect a fantastic atmosphere there as well. But, around the stadium, no one should think about anything else than the game.
"It's easy to say it, but behave like you want to be treated by others."
Asked for his reaction to the specific episode before the home game, Klopp replied: "When I heard first time about it [the fan injured] I could not describe my emotions in English. That should never have happened.
"It should never happen in the future, we have to do everything to make sure things like that don't happen anymore.
"The solution for it? Probably no one has that, but it's unbelievable that something like that can happen."
Klopp challenged the home crowd to replicate the atmosphere they produced for the tie with Roma, despite the early kick-off time on Saturday.
"We are desperate as well [as Stoke City]. We want to win the game – from my point of view, this is the game of the season. This is a final for us," he said.
"If this team doesn't deserve the most outstanding atmosphere at 12:30pm, then I don't know [who does]."