A small number of home supporters were heard singing "always the victims, it's never your fault" during the club's 4-0 victory over Wigan Athletic.
The news comes just three days after the release of the Hillsborough report, which cleared Liverpool supporters of any blame in the 1989 tragedy in which 96 supporters died.
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"It is now up to the fans to respect that."
The two clubs have historically had a bitter rivalry with both teams enjoying large periods of dominance at the top of the English game.
United and Liverpool face each other at Anfield next week and Sir Alex Ferguson said on Friday that he is hopeful of an end to the hostilities which have known to tarnish the relationships between the two clubs.
He told reporters: "We are two great clubs, ourselves and Liverpool.
"We should understand each other's problems. Maybe a line will be drawn in the sand in terms of their behaviour towards each other."