He later confirmed that the influential Irish midfielder will be out for four to six weeks.
David Beckham suffered a knock to the ankle in the closing stages of the game, and was carried off with ice packed against it.
"It's too early to say on Beckham," said Sir Alex after the game.
"He took a knock to an ankle and will probably have an X-ray tomorrow.
"It's a sore one. We don't know how serious it is yet though."