The Hoops took a 52nd-minute lead when Adel Taarabt and Kieron Dyer combined to tee up Jamie Mackie, who fired past Anders Lindegaard to score his first Premier League goal of the season.
However, United struck back through successive corners, with Jonny Evans and Darren Fletcher both netting in the space of four minutes to reverse the deficit.
Newly-appointed Hoops boss Harry Redknapp, who was in the stands at Old Trafford, watched his new side run out of energy as the match reached its conclusion, and substitute Javier Hernández completed the win with a clinical finish.
“We played for 10 or 15 minutes,” Ferguson told BBC Sport. “That was the sum total of our real performance from Manchester United.
“Of course it is frustrating we keep ending up in that position but when they scored it definitely sparked us up.”
Ferguson reversed special praise for Fletcher, who completed his first Premier League match since returning from a prolonged absence with ulcerative colitis.
“Everyone is delighted [for Darren],” he added.
“It has been a long road back for him. It is the first time he has played twice in one week. He didn’t let us down again. He never does.
“It is lovely to have him back like that. We will look at Wednesday but he has made a great contribution today.”