Brown scored his first goal for three years to set United on the road to their emphatic victory. Cristiano Ronaldo and Nani completed the scoring late in the second period.
Ferguson added: "It was a brave header from Brown for the first one, he doesn't get many but that was excellent. In the end we controlled the match and we were the better team, that is the real key.
"We started to get the breaks, Ronaldo could have had a hat-trick, Wayne Rooney could also have had a hat-trick, they both had one-on-one chances with the goalkeeper.
"In the end we should have finished them off earlier. On the day, once we had the second goal that was it. I feel that 3-0 was not a flattering score, we could have got more.
"It was good to play like that and beat our biggest rivals, we did our job and have three more points and a good goal difference."