The Ligue 1 side parted ways with Baup after their 1-0 loss to Nantes on Friday left them sitting fifth in the French top flight.
Sporting director Anigo will take charge for the next four games, the first of which is the tough task of Borussia Dortmund in the UEFA Champions League on Wednesday.
Anigo said it was unnecessary to make drastic changes, wanting his squad to become more positive after three losses in their past four games in all competitions.
"I directed my first training session this morning. I know the players. I've been already here a year and a half," he said.
"I worked with Elie. I know the players. I know the work he did with the team up to now. Maybe we have to change their state of mind. We don't have to throw everything out.
"The main responsibility belongs to the players. Normally they have a positive state of mind, but they have to find it again."
Marseille will finish bottom of Group F after losing their first five matches in Europe this season.
Anigo said his players needed to take some blame for their poor results and warned he may be unable to turn it around.
"I said to the players this morning that they have to share responsibility with the coach. It's the same at every club, when there are not good results," he said.
"But I'm not Mr Bogeyman. I'm here to bring something different. Each person has his own sensitivity, his personality.
"Elie had qualities. I have other qualities. For the next four games, maybe I'll try new things, but it might not work."
