Rooney tapped home on 34 minutes to give United a winning start to the season after his header had hit a post.
And the United boss told Sky Sports: "We had some good opportunities and played some good football and in general I am satisfied with the result.
"Is Rooney capable of 20 plus Premier League goals? He is capable of that without question.
"You always need two or three of your strikers to get over the 20 goal mark.
"It has always been an advantage over the years for us and Wayne is capable of doing that."
Meanwhile, Ferguson confirmed Michael Owen will have chances to start for United in the coming weeks.
Owen came off the bench in the second half and only a fine save by Blues keeper Joe Hart denied him his first league goal for the Red Devils.
"Owen made a great run and the keeper made a great save. But he will get his goals, no question about that," said Ferguson.
"I started with Rooney and Berbatov today quite simply because they were at the club last season and were regular players and you've got to give them an opportunity.
"Michael will get his chances. There is no question about that. There are plenty of games coming up in the next few weeks to give him his opportunity and he will take them."
Rooney was also pleased to make a winning start, saying: "I thought at times we played some good stuff. Birmingham sat back in the first half and made it difficult for us but we created enough chances to win the game.
"We couldn't get that second goal. They defended well. The second goal would have killed the game off but at 1-0 there is always a chance of the other team getting a result."
Despite the narrow defeat, Birmingham manager Alex McLeish took plenty of positives from his side's performance against the defending champions.
He said: "On another day we may have taken something from the game.
"I know United had a couple of chances and Sir Alex will be talking about the ones they missed.
"But it is the most we have created here, certainly from my experiences here. I was disappointed we didn't quite nail one of the chances.
"We worked hard and the organisation of the team was great and they applied themselves brilliantly within the system.
"They showed they are a team that never gives up."