Juan Mata's deflected strike three minutes from time gave the Blues a 1-0 win over a below-par United at Old Trafford, with Rafael sent off in the closing stages.
Chelsea had the upper hand throughout against a United side who appeared to have let their intensity levels drop after securing their 20th domestic title.
Ferguson told MUTV: "I am disappointed. I think we have put the tools away. It looked that way to me.
"We made some changes of course. We needed to give (Tom) Cleverley, Anderson and Anders (Lindegaard) a game. But there was no edge to our game, Chelsea were the better team."
When asked if team had mentally switched off after winning the league, Ferguson said: "I think so. That has a lot to do with it. It has been a long season.
"The final big effort was last week against Arsenal. Here, the edge to the game was off."
Ferguson had no complaints about the goal. He said: "I don't think Wayne (Rooney) was fouled (prior to the goal), but the referee was giving us nothing anyway. It was a bit lucky, the goal, it was deflected off Phil Jones. It was so late in the game there is not a lot you can do about that."
United ended the game with 10 men after Rafael's dismissal for kicking David Luiz.
Ferguson told Sky Sports: "Unfortunately it was controversial, it is like that a lot of times when you play against Chelsea. But we can't complain, we didn't play well enough."