Les Phoceens were dumped out at the last 32 stage after a spectacular 5-4 defeat to Nice at the Stade Velodrome.
"On the one hand, we scored four goals, so some of the players did their job," Anigo said in his press conference. "But on the other hand, we conceded five, which means that certain others did not do theirs.
"We gave them things that we should never have given away. It is more just a disappointment than a hammer blow. There were massive individual errors that I can do nothing to defend, so bad were they."
Marseille travel to AS Monaco in their next match on Sunday.