Carlos Tevez put Manchester United ahead from £30m new boy Dimitar Berbatov's pass, but Wes Brown's own goal put Liverpool level before substitute Ryan Babel's late winner.
Ferguson said: "You don't expect that from Manchester United. When we have a bad day we usually still get something from the game.
"Overall, they were the better team. Liverpool produced a performance of tackling, hassling and getting about us.
"The source of our defeat was not coping with the hassling and the tackling. You have to give them credit for that - but at the end of the day, we should cope.
Phelan admits Man Utd 'did not perform'
"We started excellently, and it was a wonderful ball from Berbatov for the goal."
Liverpool ended a run of five successive defeats against United and Ferguson said: "The difficulty of holding a record like that is that it gives the other team a big incentive every time they play you."
The United boss was unhappy about Vidic's dismissal, saying: "Carragher was making those challenges all day long, and no fouls were given.
"We had several bookings and a red card. Is that a reflection of Man United being a dirty team? I don't think so. I think the crowd plays a part."
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