Darren Bent scored a stoppage-time equaliser to salvage a draw for the struggling Cottagers, who had taken the lead through Steve Sidwell in the 19th minute.
United hit back twice in two second-half minutes through Robin van Persie and Michael Carrick and were poised to snatch the points until Bent rescued a dramatic point.
“We went out and tried to win. We crossed it, passed and tried to get through but we didn’t quite have the finishing touches,” Moyes told Sky Sports 1.
“If we had got a goal early on it would have completely altered the game.
“The more we went to score they had a couple of chances and one they went to score from.
“We deserved to be in front. Quite often at Old Trafford, we lose a goal and end up chasing the game. We deserved to win the game and three points but you don’t always get what you deserve.
“We kept knocking at the door but it wasn’t enough.”
Moyes does not sound like the coach of a big club where the expectations are to win every week and his excuses are starting to wear thin on him.
United’s game plan was get the ball out wide and cross it. And they did that an incredible 81 times on Sunday. But that is not a successful plan if less than 20 of them find a red shirt in the penalty box. Unfortunately when United needed a plan B, a different plan to break down Fulham’s defense David Moyes did not have one.
Even if you don’t have the players to quite follow out your instructions, and these are the defending champions don’t forget, it is Moyes’s tactical naivety that has to worry the United fans and board the most. Moyes’s in-game decisions are poor, especially compared to the really good managers like Mourinho, and United are continually out-coached when they come up against the better teams.
I like David Moyes, but I am beginning to wonder is he is really good enough for the Manchester United job.