The former Barcelona player was red-carded after a clumsy tackle on Abdallah Sima when he was considered the last man by referee Bastien Dechepy.
It was the fastest card – yellow or red – shown in Ligue 1 since Opta started collecting data in the league in the 2006-2007 season.
Defender Todibo clearly felt there was cover, with Dante also in close attendance to Sima when the challenge was made.
The 22 year-old reacted on Twitter, writing: "A refereeing decision that shocks me and condemns my team to start the match with a big disadvantage.
"The decisions of the referees at the start of the season are very questionable, even scandalous and I hope that the @LFPfr will do something to remedy it."
It remains to be seen what the Ligue Professionnel de Football makes of that message, and whether the accusation might serve only to compound Todibo's problems.
There was dismay at the red card in the Nice ranks, with captain Dante frustrated to see his team down to 10 men so early.
Nice went on to lose 1-0, with Nabil Bentaleb getting the only goal shortly before half-time. Angers also had a player sent off as Sofiane Boufal saw red in the 62nd minute for a second bookable offence.
Dante told Prime Video: "When you receive a red card after a few seconds of play, of course it gets bizarre.
"It doesn't happen every weekend. It got us in trouble. We were really well prepared to win this match, we wanted to put some intensity into the first quarter of an hour."
Nice made a number of high-profile moves in the transfer window but have made a surprisingly slow start to the Ligue 1 season, winning just two of their opening eight games.