Alex Ferguson and Brendan Rodgers hope the Hillsborough tribute before Manchester United's 2-1 win over Liverpool at Anfield will end vile chants by both sets of fans.
However, incidents after Sunday's Premier League match suggested some supporters had still to get the message.
After the final whistle, when most Liverpool fans had left the ground, a few home supporters ran across the main stand near to where United followers remained on police orders and started making airplane gestures.
This was in relation to the 1958 Munich air disaster, which killed 21 people including eight United players. Some United fans then responded instantly with chants of "Always the Victims" and "Murderers" in a reference to the fact Liverpool were playing during both the 1985 Heysel disaster in Brussels, where 39 Italian and Belgian fans lost their lives during a European Cup final against Juventus, and Hillsborough.
"What was done at the end I cannot comment on as I didn't hear or see anything," said Liverpool manager Rodgers.
"But it is on the field where competition should be and everything else, songs from Liverpool or Manchester supporters, any of us that have any human decency don't like to hear that.