The result virtually guaranteed the Red Devils a place in the Champions League knockout phase with three games remaining.
But it may come at a price, with Kagawa due for tests to discover the extent of the problem.
"Kagawa twisted his knee," Ferguson said. "He struggled on for 20 minutes but we will assess in in the morning because we don't know the extent of it at the moment."
With goalkeeper Anders Lindegaard also ruled out for a week after suffering a thumb injury in training, Ferguson is likely to be down on numbers for Sunday's crucial Barclays Premier League trip to leaders Chelsea.
Of more concern to the United boss is his team's inability to keep the opposition out.
For the eighth time in 12 games this season, United found themselves behind.
Indeed, with Alan netting twice they were two adrift before they hauled themselves back into the game.
Two goals from Javier Hernandez either side of Jonny Evans' second in three games gave United their win.
However, with Chelsea to come twice, and a Premier League home game against Arsenal before the rematch with Braga in a fortnight, Ferguson knows his team could be in trouble unless he finds a solution.
"I can't get to the bottom of it, I am afraid," he said.
"If you analyse the goals we are losing, they have come from throw-ins, crosses, cut-backs - all sorts. And they are finding players free in the box.
"It is difficult to put your finger on it, and it is a concern because it is making it difficult for us."
Ferguson reserved particular praise for Hernandez, who found it difficult last season after a stellar debut campaign and is most at risk from Robin van Persie's arrival from Arsenal.
"The boy is improving all the time," Ferguson said of the Mexican.
"His goal ratio is fantastic and the way he bent his run for the second goal was terrific.
"He is a fantastic trainer and he has given me a problem, which is good."