Following Wednesday night's 1-0 win over Galatasaray, United are now focused on the trip to Merseyside. It is Liverpool's first game on home soil since the damning verdict on the Hillsborough tragedy was released last week and already there are fears about supporter conduct given some United fans engaged in anti-Liverpool chants last weekend against Wigan.
Wednesday night's game passed without incident though and Vidic believes it will be the same on Sunday, as he said: "I don't think we should put so much pressure on our fans. People always try to make a big thing out of a small one but I don't have any worries. We have shown many times in the past and I think we will be proud of them."
He added: "The big teams respect each other and we are going to play football."
United will head to Liverpool without Wayne Rooney, who is still not fit despite reports he had resumed training after recovering from his badly gashed thigh.
Darren Fletcher will be available though after making his comeback after 10 months out with a chronic bowel condition.
"The supporters recognise what a tough time he has had for the last year," said manager Sir Alex Ferguson. "They gave him a marvellous reception.
"He has been out of the game for a year, it took him one or two minutes to get going but he can only be better after that."
Fletcher's presence was required to settle a few nerves as an unconvincing United laboured to victory.
Michael Carrick's seventh-minute goal proved enough but Galatasaray were denied two good penalty claims, twice hit the woodwork and also forced an excellent double save out of David de Gea.