It is a result which will bring yet more criticism, and Moyes faced pointed questions after the match over his side's one-dimensional attacking style, namely endlessly throwing balls into the box.
"One of the big things about Manchester United is that they do play with width, they do cross the ball, its in their genes here," the Scot argued, though he admitted he was worried about his side's struggle to find a way through a Fulham defence that had conceded 53 goals in their previous 24 league matches.
Moyes was just as concerned about a "mental softness" which he thinks his charges displayed in the dying stages. After delivering cross after cross into the Fulham area, Robin van Persie turned home from close range and Michael Carrick made it 2-1 to United 80 seconds later.
But although United had just 15 minutes to hold on to their lead, they failed miserably as Darren Bent nodded in from barely a yard out following a Fulham break. "You could say we maybe had a mental softness in that we didn't see the game out and get the job done," Moyes said. "When we went 2-1 up they left us with the ball. It was just a case of playing out time and we gave away a diabolical second goal. It was a game we should have easily seen out. We were comfortable. We weren't under any real pressure."
There were a few frank calls from the terraces at full-time. Boos and whistles could be heard, and although they were not widespread, patience is starting to run out for some United fans who are used to seeing their team bring home trophy after trophy every year.
United have dropped 18 points at home already and on their travels they have lost to Liverpool, Manchester City, Stoke and Chelsea.
When asked whether he could have seen the season going as badly this when he took over from Ferguson, Moyes' reply was: "Probably not, no."
There was a similarly downbeat answer from Moyes when he was asked whether his team could finish in the top four. "We will do our best," he said, though his reply smacked of resignation. "We have a good team and there will be very few teams desperate to play Manchester United, that's for sure."
The worst aspect of this failure was that on paper United could not have wished for better opponents. Fulham were rock-bottom of the Barclays Premier League with the worst defensive record in the division. Five days earlier they were knocked out of the FA Cup by Sheffield United, who are in the Sky Bet League One relegation places. But the visitors took just 19 minutes to open the scoring and they then survived an onslaught from United to eventually come away with a 2-2 draw.
In an astonishingly unsubtle tactical choice, United threw in a record 81 crosses into the Fulham box, but with 6ft 7in centre-back Dan Burn in the away side, Rene Meulensteen, the former United coach now in charge of Fulham, said his team were well prepared for everything the hosts threw at them.
"When I saw Manchester United today I thought the game plan was quite straightforward - get it wide, get it in," said Meulensteen, who walked away from Old Trafford last summer following a long spell among Sir Alex Ferguson's backroom staff.
"If you're well organised and the goalkeeper is in good positions to come and collect the ball it can be easy [to defend against]. You need a little bit of creativity and a bit of variety at times to open [teams] up.
"It was partly straightforward. We know that we had to be more compact and tight in wide areas because United would cross the ball a lot."