Manchester United say they "deplore" the anti-Liverpool chanting which occurred briefly at Old Trafford during the 4-0 win over Wigan.
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 on Saturday afternoon 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 today's 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."
The Manchester United Supporters Trust have backed Ferguson's call for an end to chants mocking the Munich air crash and Hillsborough disaster.
MUST chief executive Duncan Drasdo said: "Following this week's developments and release of revelatory information on the Hillsborough tragedy, MUST wishes to make it absolutely clear that just as we condemn chants mocking the Munich air disaster we also condemn any chants relating to Hillsborough or indeed any other human tragedy.
"We did hear the usual anti-Liverpool chants at the match today but we're pleased to say, despite some reports to the contrary, there was nothing that was specifically referencing Hillsborough.
"Any attempt to suggest otherwise is irresponsible given the forthcoming fixture between the clubs and furthermore risks needlessly upsetting the bereaved families further at a time when they are understandably trying to find closure.
"We enjoy a fierce rivalry but these issues transcend that rivalry.
"We agree 100% with the statement made by Sir Alex Ferguson - this is the time for supporters of these two great clubs to represent their clubs with the integrity and honour that our glorious history demands."