The Red Devils entered the clash with their bitter rivals off the back of losing two of their last three matches in the league, but they could not bounce back at Old Trafford, as Liverpool ran riot in a five-goal thrashing.
Maguire has said that the team's performance was "nowhere near good enough" and has urged the players to "look in the mirror when we go home tonight".
"We apologise to the fans, it was nowhere near good enough for this club. They stuck with us right to the end and we appreciate that but as a club we have to do better," Maguire told Sky Sports News.
"I am so disappointed, we gave them so many chances. They were so clinical, we had a lot of chances ourselves but I am a defender and to concede four in the first half especially at Old Trafford is nowhere near good enough.
"As a player I know myself. I'll be looking at myself and my individual performance. We have to stick together, there is no point blaming each other but look at ourselves. Look in the mirror when we go home tonight and think where we can do better.
"To lose to Liverpool in any game of football hurts. The rivals, the way we lost the game, to be 4-0 down at half time in front of our fans, like I say it is not good enough."
Man United will be looking to bounce back from the bitterly disappointing result when they continue their Premier League campaign away to Tottenham Hotspur next weekend.