Having been thrashed 5-0 by the Reds at Old Trafford under former boss Ole Gunnar Solskjaer earlier this season, United have conceded nine goals without reply against Jurgen Klopp's men this term.
Only once in its league history has United suffered a heavier combined defeat against one opponent across a single season, losing 11-0 over two games against Sunderland in 1892-1893.
They managed only 28 per cent possession and recorded just a single shot on target during an abject display against the title-chasing Merseyside outfit, leading Fernandes to say that apologising to the club's fans "will never be enough".
However, he rejected accusations of a lack of effort from some United stars, saying they came up short on quality, rather than application.
"Obviously it's a bad result once again, there's not much that I can say, I think apologising to the fans will never be enough, but it's all we can do now," the Portugal international said.
"They do not deserve that we play in this way, they deserve much more from us, the way they support us until the end, the way they stay to applaud us, they deserve much more, and we know we have to set the level much higher, it is what it is.
"I think everyone runs, I think every game we have effort from everyone, I don't want to even think that someone doesn't give 100 per cent of themselves for themselves and for the team.
"We have to say things [amongst the squad], but it has to be kept in the dressing room. We know that there's not much we can do, but now the game is over we have to think of the next one, and it's a tough one again [at Arsenal on Saturday].
"Liverpool is fighting for the title, that is the difference, we are fighting for nothing at the moment, so you can see difference by the points, I don't need to be here saying about the difference of the levels.
"We have to look at ourselves, we have to look inside from the top to the bottom, and understand what is going wrong."
This is the sixth time a team has done the Premier League double over United without conceding a goal, with Liverpool responsible for three of those, also doing so in 2000-01 and 2013-14.
Meanwhile, the Reds are unbeaten in their last eight Premier League games against their old rivals, winning five and drawing three. No team has ever had a longer run without defeat against the Red Devils in the competition (level with Chelsea between 2013 and 2016).
Ralf Rangnick's side is now three points behind fourth-placed Tottenham in the Premier League table having played one game more than Antonio Conte's men, and looks like the outsider to secure Champions League qualification just a year on from finishing as Premier League runners-up.
However, Fernandes refuted the idea that the team were simply waiting for the season to end, saying everyone at the club had to continue fighting until the end of the campaign.
"No, no [we cannot want the season to end]. That cannot happen, we are a big club and are competing until the end," he added. "We have to compete, if someone doesn't want to compete, they can sit out and not be a part of the team.
"Nobody can put their heads down and think that they just want their vacations or whatever, all of us have to understand that we have something to fight for, at least in the matches."