"We lost the first goal by not defending properly," said Ferguson, whose side have now fallen four points behind leaders Chelsea.
"They got a lucky break when the ball came off Jonny Evans, nonetheless, you can't allow the left-back to get as far as that.
"It was a poor start and from then on, we were against the wind until half-time came along and we were able change things a bit."
Rooney's introduction made a difference that at least allowed Ferguson to put a positive spin on the game.
"We were brilliant in the second half, really unlucky, hit the post, hit the bar, balls scrambled clear. We just dominated it," he said.
"It was a fantastic performance. Thank goodness I am able to say that after watching the first half."