Play was suspended after Italy striker Balotelli, 29, picked up the ball in the 54th-minute.
Brescia team-mates and the officials persuaded him to stay on the field.
Balotelli wrote on Instagram: "The 'people' of this curva who made the monkey chants. Shame on you, shame on you, shame on you."
The former Manchester City and Liverpool striker included a video of some supporters making the chants in his Instagram Stories.
He added: "In front of your children, wives, relatives, parents, friends and acquaintances... shame.