The German is no stranger to city rivalries. He managed Borussia Dortmund during the fiercely contested Ruhr derby games against Schalke 04 in the Bundesliga.
"Before I went to Dortmund there were lots of red cards in derbies. I don't want to see this. Not to show 'I am the man'," Klopp told reporters on Tuesday.
"Maybe one or two fans want to see stuff like this, but it will never help. I understand aggressiveness only in one way, and that is being prepared to hurt yourself, not somebody else."
Liverpool face Villarreal in the semi-finals of the Europa League next week, but Klopp said his players had banished European ambitions from their minds and were concentrating on defeating their local rivals.
"Nobody in our dressing room is thinking about the Europa League," he said.
Liverpool are currently eight in the domestic standings, three places above Everton, and Klopp, who made 10 changes for their last game against Bournemouth, said he was not planning to save his best players for the semi-final first leg on April 28.
"We have a situation where we can change," he added. "We felt good before the Bournemouth game and it will be the same against Everton. No one will be rested.
"We have eight games, hopefully nine games to play. It makes no sense to push the same 11 players through all these games.
"It doesn't mean we have to rest players for two weeks. If somebody thought when they saw our line-up for Bournemouth that we didn't want to win the game, then it is the biggest misunderstanding in history.
"Liverpool is a very big club. It's a big difference between seventh or sixth or fifth (in the Premier League). We need to try everything to get the best position we can get. We could be fifth."
(Reporting by Simon Jennings in Bengaluru, editing by Larry King)
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