United gave away a penalty and had Paul Scholes sent off early on, before Wayne Rooney's late dismissal topped a dismal afternoon in the capital.
Following their loss to Liverpool last week, Ferguson's side have now succumbed to two defeats in a row, and the veteran manager admits that dropping six points in eight days is tough to take.
"I'm disappointed," Ferguson told Sky Sports.
"I was disappointed with the first half, we didn't get started at all and that's cost us the game.
"But in fairness to the team, in the second half they responded to the half-time talking and I think that we were unlucky not to get something out of it.
"If we'd have got the goal then we could have maybe even have won it. We could have played with a lot of patience and discipline and waited until the last part to have a charge, but in fairness to them they kept going and full credit to them."
Pivotal decisionScholes' dismissal for the penalty had seemed a fair call by the referee, but Ferguson has cast doubt over the decision by noting that the midfielder was little more than a yard from the header when it was made by Bobby Zamora.
"It's close to him so he could have easily not given it, but it's Phil Dowd so what do you expect?" Ferguson remarked.
"The second one I have to say, did he (Rooney) throw the ball at the referee? The ball was thrown direct to where the free-kick was taken and did it hit the referee? No, the ball didn't hit the referee.
"Was it thrown in anger? Yes, because he wanted the game hurried up, he threw with pace to get the game going."
Title pressureIf Liverpool can overcome Aston Villa in Sunday's late kick-off then the gap between United and their rivals will be shortened to just one point - although United will have a game in hand.
Many Red Devils fans may well be feeling nervous at the ever-lessening lead that Ferguson's charges hold, but the Scot insists that his side are still in the driving seat for glory in May.
He added: "If you lose games in March and April then it can cost you, but fortunately we have a little slender lead at the moment."