Cristiano Ronaldo's strike on 51 minutes was enough for United and Ferguson said: "On reflection, that is the best side we have played this season.
"In the first half we were lucky, although we did carve out a few chances of our own. I couldn't wait to get in to half-time.
"Birmingham were very athletic, very aggressive, very quick about the pitch and even at 1-0 I was still praying we would get through the match.
"We had opportunities but Birmingham, in the first half, had even better ones."
Ferguson was full of praise for Ronaldo, who scored his first league goal of the campaign in what was his 100th Premier League start.
He said: "Ronaldo was sensational again today. The boy is so talented. His capabilities are unending.
"The goal might have come from a mistake but his composure was excellent."