On a horror night for Chelsea they eventually lost 4-3 on penalties after a 3-3 draw at the end of extra-time.
Now it is Blackburn who will face Aston Villa in a two-legged semi-final in January for the right to go to Wembley.
The Ewood Park club inflicted only the third defeat of the season on the current Barclays Premier League leaders.
But a string of debatable decisions by Ancelotti contributed to Chelsea's demise, including using all three substitutes at the bench before injury reduced them to 10 men for almost 50 minutes of the match.
"But in the first half they did not play well. That is why I used all three substitutes, it is not something I usually do.
"Then we were unlucky to have Salomon Kalou injured in the second half, and that meant we were left with 10 men. It was just unfortunate, but we still played well with 10 against 11.
"As for using Kakuta for that last penalty, it was my decision. I have seen him take good penalties during training, and I felt he could handle it."
A Brett Emerton cross deceived Henrique Hilario for Blackburn's equaliser, with an extra-time penalty from Benni McCarthy putting them ahead before Paulo Ferreira's equaliser in the final seconds forced penalties.