Yaya Toure fired City into their first final since 1981, where they will play the winners of Sunday's clash between Bolton and Stoke.
But Ferguson believed his side had contributed to their own downfall.
"The first 15 minutes after half-time cost us the game," Ferguson told MUTV. "Slack moments. Edwin (van der Sar) had a bad kick out and Michael Carrick couldn't hold it and it was a goal.
"From then on, they were defending apart from a couple of counter-attacks. It's disappointing as we should've been ahead in the first half as we were the better team."
Source: PA
Source: PA