The Premier League match is the first at Anfield since the Hillsborough Independent Panel published its damning report that exonerated Liverpool fans, detailed extensive failures from the authorities that led to the tragedy in 1989 and exposed the scale of the cover-up operation that followed.
Liverpool will mark the occasion by paying tribute to the 96 fans who died following the events of April 15, 1989, but there are fears that a minority of United fans will sing anti-Liverpool songs, as they did last weekend against Wigan.
Vidic has now Ferguson vows backing for Liverpool.
"I am aware of the sensitivity of the day," Vidic said. "Everybody is. There is a lot of talk in the papers and the media. I think our fans will respond well.
"The whole country is on test in this one. All over the world they will be watching this game. It is probably the biggest derby in the world and we have to show we are capable of keeping a good atmosphere and being a good example to the kids.
"There is a lot of history with these two clubs. I think we should respect each other because we are big clubs and clubs that are respected in the world. We have to be on top of the bad situation and behave well and, I would say, be an example.
"I've been here for seven years and I think our fans always behave well and I think they will do it again. It is difficult to control all the fans but I think most of them are aware of the responsibility. On the pitch we have to take responsibility and play football. After this game everyone should be talking about the football and that's all. I hope that will be the case."
Tensions are also running high after Luis Suarez was found guilty of racially abusing Patrice Evra last season and then subsequently refused to shake the United defender's hand prior to a match in February.
"To be fair, I don't want to think about that," Vidic said. "Obviously we want to focus on the game. We have a theme, what happened in history about the fans and we have to respect that day. Obviously we cannot come with any other issues, we just come there play football.
"If they shake hands, they shake hands – I don't think it's the most important thing in the world. I think it's important to not do any stupid things in the game, to go there and play football – what we dream of, to play that derby and to be all about the football, not about the fighting or any other things."