Klopp added: “We should use this opportunity on the pitch to make sure all the nice stories are written about what happens on it, and not around.
“Big respect is what this sport stands for and you face your biggest opponents and play football against them. That is the battle we have, that is where we should show who is the best and create a special atmosphere.”
Last season’s games were marred by chanting about Munich and Hillsborough.
In 1958, eight United players were among 23 people who died after their plane caught fire and crashed in Munich.
Ninety six Liverpool fans died as a result of a crush during an FA Cup semi-final with Nottingham Forest at Hillsborough in 1989.
“In football you have some football tragedies,” said Mourinho. “You lose a big match or make a mistake. You can make fun of it.
“Human tragedy is something much more serious. It is the last thing someone should use in a football pitch. Really big tragedies are serious.”
Mourinho’s side go into Monday’s game – which kicks off at 20:00 BST – sixth in the Premier League with 13 points, two places and three points adrift of Liverpool.
The impossible job? Probably. Use our shortlist and pick who you think would make the greatest combined post-war Liverpool-Manchester United XI.