Merseyside Police have vowed to crack down on any troublemakers to avoid a repeat of the incidents before the clash with Manchester City in the quarter-finals, when missiles were thrown from within a crowd of Reds supporters at the visitors' team bus as it made its way to Anfield.
Klopp does not want Roma to receive the same welcome and has urged fans to show their opponents the positive side of their "fantastic" support.
"In the stadium – do it again, and do it better. Out of the stadium, please show the respect we need to show," he told a news conference.
"This is such a fantastic football club, an outstanding football family known for fantastic atmospheres all over the world. We don't need to throw whatever at the bus of the opposing team.
"Please, show [Roma] the respect they deserve. We are only opponents on the pitch – I feel this wonderful city can show [the world] how nice Liverpool people are, and the spirit of the club."
Klopp has also challenged the Anfield crowd to create an even better atmosphere than they did in that 3-0 win over City on April 4.
"The good thing at Liverpool is I don't have to tell them what to see; they know it already," he said. "They create one of the most special atmospheres in world football.
"They're more experienced of this situation than we are. I don't know if the atmosphere against Manchester City can be bettered but, if so, let's try.
"If you cannot enjoy these moments, there's something wrong with you. I don't have to say anything – I know they will be perfect."
Hendo on the #LFC fans: “At Anfield the atmosphere's unbelievable. It gives us a great lift and it's really helped us on these big occasions. I'm sure the atmosphere will be brilliant and we need to put in a performance to match it.”
Watch live and free: https://t.co/fRCf4TEyVW pic.twitter.com/ix8LBAUToZ — Liverpool FC (@LFC) April 23, 2018
Captain Jordan Henderson also hopes the fans can inspire another top European performance, saying: "Obviously at Anfield the atmosphere is unbelievable. It gives us a great lift as a team and it's helped us on big occasions so far.
"Hopefully, the crowd will be unbelievable, but the performance needs to match
"They'll maybe ask different questions to City but we've played a lot of good sides in Europe who have asked a lot of questions of us, and we've answered them so far
"They're a strong side – we need to be ready and keep doing what we've been doing well. We need to keep playing at a high intensity, keep creating chances and scoring goals."
Roma produced a huge shock by knocking out Barcelona in the quarter-finals on away goals after a 3-0 second-leg win, but Klopp does not think there is any added pressure on his side simply because they are the favourites for this tie.
He added: "I thought in the first second, when I heard the 3-0 result, it wasn't possible. But it is. Now we play against each other, so maybe our situation is similar.
"What's really important is we can enjoy our own football – there’s only one team that can win it, but it’s a long season. Our job is to show the best we can.
"People talk to me about pressure, about a once-in-a-lifetime opportunity, but it's not like that. Even for me it would be the second time to the final, so it shows what is possible."