Last season, both clubs were fined by UEFA for crowd disturbances and supporters engaging in illicit chanting when they met in the last 16 of the Europa League.
The chants aimed at Liverpool supporters concerned around the Heysel and Hillsborough stadium tragedies while those directed at United fans referenced the Munich air disaster in 1958.
"In football, we have some 'football tragedies', which is the big match that you lost, the mistake that some player did and you can make fun of it in a positive way," the Portuguese told reporters.
"But the human tragedy is something much, much more serious and I think is the last thing somebody should use on a football pitch.
"These need our respect, so I would be really sad if in such a big football match that was a negative point."
The clubs issued a joint statement on Thursday warning supporters to behave and Mourinho reinforced the message at a news conference on Friday.
Mourinho said he was looking forward to the atmosphere at Anfield, comparing the match to the other derbies he has experienced during his managerial career.
"I always like to play at Anfield," said Mourinho, who faced Liverpool many times as manager of Chelsea.
"I won many times there, I also lost. I won big matches, I lost big matches. I cannot say I like to go there because I'm always successful because it's not true. I like to go there, I like the atmosphere.
"Being Man United manager obviously means something more because we cannot compare the historical rivalry between my previous club and Liverpool, Man United and Liverpool," he added.
"In the end, it's just a big match. It can be comparable to Milan v Inter Milan, (Real) Madrid v Barcelona, maybe Porto v Benfica, maybe comparable to one of these matches."
The manager was at pains to make clear that the outcome would not define United's season, but said he appreciated how much the fixture meant to supporters.
"I'm in England for a long time," he said. "Obviously I never played this match but I played many times against Liverpool, United. I understand the dimension of the clubs and now I understand better the history between the rivals.
"The season for me is not about the Anfield match though, or Old Trafford in January. It's about many matches."
Mourinho also gave short shrift to questions about Wayne Rooney's mindset after the United skipper was dropped from England's starting line-up during the international break.
"England is not my problem, but he is prepared, training well and is positive," the manager added.
(Reporting by Simon Jennings in Bengaluru, editing by Ed Osmond)
