Florent Malouda scored one while Frank Lampard scored the other two for Chelsea.
Ancelotti told Sky Sports: “We showed good play for 90 minutes. It was a bit more difficult in the second half, but that is normal when you play against a good team like Birmingham.
“We had fantastic individual performances like John Terry and Malouda and Deco. It is a good moment for us.”
Ancelotti admits he is looking forward to have Didier Drogba back in his starting XI.
Drogba along with Salomon Kalou returned from the African Cup of Nations on Wednesday.
The duo could feature against Burnley on Saturday evening.
Ancelotti said: “The message is that we need Drogba back because he is a fantastic player.
“I want to thank my players, but we need Drogba back for the future.
“I don’t know if he will be ready. We have to do a check tomorrow (Thursday), and also Kalou, and then we will make a decision.”
He added: “Our philosophy and aims won’t change – to play good football and win. We won’t change. We’ll maintain the same system.
“I’m happy Drogba will be here with us tomorrow morning. He had a fantastic start to the season.”
