Both forwards had been required to link up with their national side in advance of January's African Nations Cup but Ivory Coast have delayed the date of their departure until December 29.
"We asked the national team and the coach agreed with us," Ancelotti said. "Anelka cannot play against Fulham; he will play the first game in the new year."
Chelsea failed to score for the first time in 34 games in Saturday's match at St Andrews and have now won just one of their past seven games. However, given that their lead at the top of the Premier League has been extended to five points ahead of Manchester United's game against Hull City, Ancelotti was reluctant to condemn his side.
"It's not a good result for us considering what we did on the pitch because Chelsea played well, had a lot of chances, had a lot of heart and the keeper for Birmingham made some fantastic saves," Ancelotti said. "We are disappointed with the result but not with the team.
"It is not our best moment because it is not good for us to draw. But I don't see a big problem, I think we have some problems because we have two very good players out, Anelka and [Michael] Essien, and always we play good football, even today we played good football.
"Our aim is to win the title, we are in the top of the league at this moment and this is good for us. We do a good job, we work hard and we can win. It is not possible to win the title in December, you have to win it in May and we have to be ready in May."
Birmingham extended their impressive run of form when making it ten games without defeat in the Premier League and manager Alex McLeish reserved special praise for on-loan goalkeeper Joe Hart after he made a succession of saves to deny Chelsea.
"Joe has come on a ton, we talked about one or two things earlier in the season and he has improved," said McLeish. "I'm pleased for him because he is a conscientious guy, he's his own biggest critic and he wants to get better and better.
"And Chelsea had their moments. We had one or two issues, we had a little bit of luck and we put in some fantastic defending.But Chelsea have so much quality it won't be long before they start winning again. They will roll up their sleeves I'm sure."