The 70-year-old has condemned chants from Red Devils supporters concerning the disaster which were aired during Saturday's 4-0 win over Wigan at Old Trafford
Ninety-six Liverpool supporters were crushed to death during an FA Cup semi-final between the Reds and Nottingham Forest on April 15 1989 in Sheffield, though original inquests delivered a verdict of 'accidental death'.
Last week the Hillsborough Independent Panel released their findings, which cleared supporters of any wrongdoing and revealed that police had attempted to hide their culpability through a media-led smear campaign.
During United's 4-0 win over Wigan at Old Trafford on Saturday, several supporters were heard to sing "always the victim, it's never your fault" - a chant which Sir Alex has now condemned.
"I didn't hear it [the chants at the Wigan game], but everyone else seemed to hear it. David Gill heard it in the director's box and was disappointed," he told reporters.
"The chant is a new chant. It only started after the Suarez situation [when the Liverpool striker was found guilty of racially abusing Patrice Evra last season].
"But in the current climate and having spoken on Friday, asking our supporters to adhere to the policy that we want to adopt - that we're completely in support of Liverpool Football Club at this moment in time and we understand what those families must have felt during the week when they got that report - it was disappointing to hear that.
"It's a minority, though, and in society there's a minority who want to be heard. That's the difficulty you've got nowadays.
"As a club we're totally in support of Liverpool and the situation they're in. It's going to be a very emotional day on Sunday and we'll support them in every way we can."
United will face their bitter rivals at Anfield on Sunday afternoon.