United manager Sir Alex Ferguson had expressed the hope that a line could be drawn in the sand on the sour relations between the two sets of supporters following this week's damning report on the handling of the Hillsborough disaster in 1989, in which 96 people died.
The report laid bare a shocking cover-up which attempted to shift the blame for the tragedy on to its victims. It revealed South Yorkshire Police had instructed officers to change or amend their statements relating to the events of April 15, 1989, when the FA Cup semi-final between Liverpool and Nottingham Forest was abandoned as the tragedy unfolded.
United's biggest win of the season was scarred by a short burst of anti-Liverpool chanting from a small minority of home fans.
One clearly audible chant was "Always the victims, never your fault".
Ferguson's stance is shared by all senior figures at Old Trafford, who will hope the songs are not repeated when United head to Anfield on Sunday week.
A United spokesperson said the club "deplore" such songs.
In a statement, United said: "The manager has made the club's position very clear on this matter. It is now up to the fans to respect that."