United released a statement after the match in response to the incidents.
"The club deplore it. The manager has made the club's position very clear on this matter," a statement read.
"It is now up to the fans to respect that."
Ferguson takes his team to Anfield next weekend for the first Liverpool home game since the findings of an independent panel investigating the Hillsborough disaster were published this week.
Liverpool supporters were cleared of blame over the deaths of 96 people in 1989, with the panel laying the blame with South Yorkshire Police.
FA makes 'full and unreserved' Hillsborough apology
United supporters took to social media networks after the match to play down the significance of the songs, claiming that while they had been aimed at Liverpool, they related only to fallout from the Luis Suarez-Patrice Evra race row last season.
However, with the timing of the chants, the issue is particularly sensitive. The chant, which includes the words "It's never your fault, it's never your fault, always the victims, it's never your fault," was heard from a section of fans in the Stretford End early in the match.
The Manchester United Supporters Trust (MUST) later issued a statement saying that it agreed "100%" with Ferguson's pre-match words, but that the chants heard against Wigan were not about the Hillsborough disaster.
"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," said MUST chief executive Duncan Drasdo.
"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."
On Friday, Ferguson said he hoped both sets of supporters would "draw a line in the sand" in their heated rivalry, which has also seen some Liverpool fans mock United over the deaths of eight players in the 1958 Munich air crash.
"I think what will happen for that Liverpool game, I think there is such a focus on it at the moment, fans will be on their best behaviour," Ferguson said.
"I think it's a moment for those two great clubs to show why they're two great clubs. I don't anticipate any problems."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.