A late goal from Serbian striker Nikola Zigic earned City their first win over Villa for five and a half years after Gabriel Agbonlahor had cancelled out Sebastian Larsson's penalty.
Ferguson, who gave another exemplary display in midfield, said: "The manager is building a new team, brought a few new players in in summer, and they're settling in really well. I can see we're starting to close the gap on Aston Villa, certainly."
He added: "I'm just delighted we've won, we're in a semi-final now, and you never know what might happen now.
"We've shown that mentality all season where the guys never lie down and thankfully we got the victory.
"Villa had a few chances but we always felt confident we could get one."
Blues keeper Ben Foster said: "We've pretty much been concentrating on the league but it's been a fantastic run we've had in the cup.
"Get through the semi-final and you're at Wembley. For a team like Birmingham, that would be a fantastic achievement.
"In cup football, anyone can cause big upsets and hopefully we can keep doing it."