United were facing their first home defeat in 23 Champions League games after finding themselves two goals down to the Russians early in the second half.
Rooney, whose wife Coleen gave birth to baby boy Kai yesterday, was then introduced and - according to CSKA coach Leonid Slutski - changed the face of the game.
Ferguson said: "Wayne hadn't had much sleep. I would have preferred to leave him on the bench.
"He was a safety player that we knew we could have played if we needed him - he was there.
"I think his energy and confidence was very high. He makes an impact. He is such a good player and is always capable of scoring. He was a wee bit unlucky."
Slutski added: "Rooney is one of the best players in the world. He has a high level of skill as well as aggression.
"He made a difference as I thought United were moderate before he came on."