The England international scored twice in his side's 4-0 victory, netting in the 35th minute of the contest before adding his second in the 54th minute.
Bellingham was replaced three minutes after completing his brace, though, and the ex-Birmingham City youngster looked in discomfort when leaving the field.
Ancelotti has said that the 20-year-old suffered "a sprained ankle" on Saturday, and he is now a doubt for Tuesday's Champions League last-16 clash with RB Leipzig.
"Bellingham picked up a sprained ankle, they'll assess him tomorrow. I hope we can have him fit for Tuesday," the Real Madrid head coach told reporters during his post-match press conference.
"There are games he hasn't been involved in and others have come in and contributed a lot, like Brahim [Diaz] and Joselu."
Ancelotti also addressed the comparisons with Zinedine Zidane that have been levelled at Bellingham, who has now scored 20 goals and registered eight assists in 29 appearances for Los Blancos this season.
"There are things about the way he plays that remind me of Zidane, it's his extraordinary quality on the ball. Zidane may have been even better technically but Bellingham combines it with how he gets into the box. There are few players in the world who can match his movement for his first goal," he added.
Antonio Rudiger will again be sidelined against Leipzig due to a troublesome thigh problem, while Thibaut Courtois, Eder Militao and David Alaba remain unavailable for selection, but Nacho will be fit for the European fixture despite missing out against Girona with a muscular issue.
"We're pleased to be going back into the Champions League with a lead in La Liga despite the difficulties we've had so far with injuries," added Ancelotti, with his team moving five points clear at the top of the La Liga table.
"We're really excited and we're up against opposition who we must be very careful of. We have to prepare every game like we did today.
"I do what I can, I try to get the best out of the squad and the group. It's a group that keeps me incredibly motivated because there's a great feeling there and I have immense respect for them. The key is always the players because when you have quality at your disposal, it's your job to make that come through to the group.
"We're a game and a draw ahead at this stage of the season, but that's all it is: a slight advantage. We're well-placed. We've done a great job so far but the Champions League will add to our fatigue and we must continue to show commitment and the right attitude."
Real Madrid have won seven of their last eight league matches, while they have only been beaten once in Spain's top flight this term - a 3-1 reverse at Atletico Madrid on September 24.