The Italian posted a message on his Instagram page on Saturday, saying the incident was a "real shame".
"Yesterday the result against Bastia was right... we will work more and try to get our objective.. the referee was good too but I have a question for French people... Is it normal that Bastia supporters make monkey noise and "uh uh" for the whole game and no one of the "commissions discipline" say nothing?," Balotelli, on loan from Liverpool this season, wrote.
"So is racism LEGAL in France? Or only in Bastia?
Football is an amazing sport .. those people like Bastia supporters make it horrible."
In a statement on their website, Nice gave their full support to Balotelli, adding that stones had been thrown at their team bus ahead of the game.
"We are ... shocked to learn of the behaviour towards their players, especially Balotelli. The club congratulates them for remaining calm and not reacting and give them their full support," Nice said in a statement on their website (www.ogcnice.com).
The French League (LFP) said it would investigate the "incidents" in its next disciplinary commission meeting on Thursday.
Bastia were docked two points by the LFP in the 2007-08 season after fans racially abused a Libourne St Serin player during a Ligue 2 game.
Bastia did not respond to an email from Reuters.
Nice are top of the Ligue 1 standings with 46 points from 21 games. Bastia are 15th on 21 points.
(Reporting by Julien Pretot, editing by Pritha Sarkar)
