The Merseyside club host their rivals in the fourth round of the FA Cup on Saturday and the Reds coach hopes their League Cup semi-final win in midweek will lift them at Anfield
Patrice Evra, who was involved in Luis Suarez’s eight-match ban for using racist language earlier in the season, is set to play for, and captaing, the reigning Premier League champions at Anfield.
Liverpool fans are guaranteed to give the left-back a frosty reception, but Dalglish insists his players need to focus on the football aspect of the match and not get distracted.
“We want to concentrate on going out and playing football and any other sideshow is purely that, it is just a sideshow,” the Scot told reporters on Friday.
“Everyone has a responsibility to uphold the names of their respective club, and anyone who reports or comments on the game also has the responsibility to make sure they are not trying to incite trouble.
“But it is not only the fans who have to behave themselves; we have a responsibility to behave – but that is the case every time.
“I am sure everyone will be determined to make sure what's done has been done and whatever your grievance is keep it to yourself and let's get on with the game.”
Although Dalglish called for tempers to be kept in check for the match, he hopes both sides remain as competitive as they have ever been.
The 60-year-old continued: “The significance of a match between Liverpool and Manchester United is always of great importance and this one will be no different.
“It would be a huge disappointment on both sides if either team did not compete as well as they can.
“They are highly-charged matches but that is because players take great pride in the clubs they represent.
“We have to go on the pitch and compete. You cannot take away the competitive edge from a football match and we won't be taking away ours.
“But we have an opportunity to play football and that is all they [the players] want to do.”
Liverpool drew 2-2 with Manchester City on Wednesday to take them through to the League Cup final with an aggregate win of 3-2, and spirits will inevitably be riding high at Anfield.
Dalglish, who has won the FA Cup twice with Liverpool in the past, added: “We are looking forward to a fantastic match; we had unbelievable support from our people on Wednesday night and I am sure we will get the same again.
“We would be delighted if we could replicate what happened on Wednesday but we know what we are going to get from our supporters - they are 100% behind us.
“Had it not been for their support we might not be going to Wembley.
“They know their importance and we respect that importance. I am sure people can look forward to a fantastic spectacle.”