"In the first half we never got started," admitted Ferguson.
"They were lively and got stuck in and we respect that - they lost 4-0 to us a couple of weeks ago."
United were much-improved after the break but after Mark Schwarzer kept them at bay with a string of excellent saves, Zoltan Gera struck on the break for Fulham.
Shortly after, Rooney, on as a half-time substitute, saw red for allowing his frustration to get the better of him, throwing the ball angrily after Dowd ordered a free-kick to be taken again.
A bad afternoon for United improved slightly with the news that Chelsea had lost at Tottenham, meaning they remain four points behind.
Liverpool, though, can still close the gap with victory against Villa, although United will have a game in hand.
"It's disappointing we didn't meet the challenge," said Ferguson.
"If you lose games in March and April it can cost you. Fortunately we have a slender lead at the moment but not a lot and I'm hoping we come back from the internationals back to our best."
Fulham boss Roy Hodgson is still backing United to retain their Premier League title.
"I still think they are favourites, but the last two defeats have given the teams chasing them that little bit more hope," said the Cottagers boss, who oversaw Fulham's first home win over United since 1964.
"Our first half performance was quite outstanding. I didn't think we played quite as well in the second half. But we worked and fought hard.
"When you are leading 1-0 against United who have got 10 men, something of a siege mentality is always likely to creep in to your game, even though you don't want it to.
"I am really pleased with the victory. The players have deserved this. It is nice to reach that magical total of 40 points as well and I am hoping we can reproduce something like the same football in the next eight games."
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