The result continued a pitiful start to 2014, which has seen United win just three times. One of those wins, in the second leg of the Capital One Cup semi-final against Sunderland, effectively became a defeat anyway as the Red Devils crashed out on penalties.
Little wonder every bit of evidence is being seized on to explain how a team should crumble so quickly after they won the title by 11 points last term.
Manager Moyes can point to extreme instances of bad luck; David de Gea's last-minute fumble against Sunderland that cost his team a place at Wembley, or Darren Bent's injury-time equaliser at the weekend for a Fulham side who did not seem to be so bothered about scoring.
Ultimately though, the Scot acknowledges the fault lies within his dressing room.
"Winning changes it - and we have not won often enough," said Moyes, who succeeded Sir Alex Ferguson last summer.
"We are a top side.
"Anybody who knows and understands football knew that changes had to be made. Anybody who watched the game the other day and didn't think we deserved to win by a hundred miles knows nothing about it.
"There have been other games like that. But we are not looking for excuses.
"We can only blame ourselves and we need to do better."
It is true anything that can go wrong for Moyes is doing so at present.
Both Phil Jones and Marouane Fellaini are set to miss Wednesday's trip to Arsenal after being struck down by injuries that came immediately after they had recovered from different physical problems.
Robin van Persie and Wayne Rooney are still trying to find their best form after a spell on the sidelines, while both the defensive and midfield areas are operating below their best as United struggle for confidence.
Yet Moyes retains belief in his squad, for whom record signing Juan Mata has also failed to sparkle on a consistent basis.
"We have a great group of players here," said Moyes. "They have shown it previously. I see them every day and I still believe they are a great group.
"They are hurting as well. They want to improve it."
Moyes realises further additions need to be made.
Nemanja Vidic is unlikely to be on his own in leaving Old Trafford this summer, with Rio Ferdinand, Patrice Evra and Javier Hernandez among those for whom time is surely running out on their United careers.
However, Moyes does understand that until his team halt their present disastrous run, the negative angle will be found to accompany all his work.
"A lot of people are looking at the Fulham game and saying we crossed it too much," said Moyes.
"If we hadn't crossed it they would be saying we should have crossed it more.
"We are coming to terms with it. We need the fortune to change."
Some games are easier to look upon as potential catalysts than others.
A visit to Arsenal is certainly one.
United have already claimed the Gunners' scalp once this season, when Van Persie scored the only goal against his old club.
What Moyes would give for a repeat of that single-goal success against a side with problems of their own after the 5-1 hammering they took at Liverpool at the weekend.
Not that Moyes views the teams' respective problems as taking on any greater significance.
"It doesn't need anything adding to the occasion," he said.
"Arsenal against Manchester United has always been a big game. You only have to look back through the seasons to see how important these games have been.
"It is an important game for both teams."
- Sports & Recreation