The 54-year-old Frenchman left his position after just seven games in charge, having lost five matches since taking over in June.
His assistant Bernard Rodriguez, who joined with Anigo, is to take over, club officials said.
The defeat to Ahly confirmed Esperance's exit from the competition.
Holders Al Ahly guaranteed their semi-final spot after that victory over Esperance in Rades on Saturday.
Ghana-born John Antwi scored the only goal of the Group A fixture to send the Egyptian club temporarily to the top of the group with one game remaining.
Former African champions Esperance exit the second-tier continental club championship after four defeats at the group stage.
Etoile du Sahel also advanced to the semi-finals after a 1-1 draw in Bamako with Stade Malien on Sunday.
Guinean striker Alkhali Bangoura gave visiting Etoile the lead on the hour mark before the hosts grabbed an equaliser six minutes into injury time through Moussa Coulibaly.
Ahly and Etoile both have 10 points going into the final group games when the Egyptians host Stade Malien while the other match is a Tunisian derby.
In Group B, Orlando Pirates of South Africa beat AC Leopards of Congo Brazzaville 2-0 on Saturday to ensure both they and Zamalek of Egypt advance.
Goals from Terrence Makola and Oupa Manyisa gave Pirates the victory, earning them a place at the last four together with five-time African champions, Zamalek.
Egyptian champions Zamalek drew level with Pirates at the top of Group B with a 3-1 win in Tunisia over three-time Confederation Cup winners CS Sfaxien.
Mahmoud Kahraba opened the scoring for Zamalek in the 54th minute before Ali Maaloul scored an equaliser from the penalty spot.
New signing Ahmed Hamoudi then scored twice to seal the win for Zamalek.
Orlando Pirates will travel to face Zamalek in the final group game in September to decide who finishes top of the table.
Under the tournament regulations if two or more sides are level on points at the end of the group stage the head-to-head record is used to decide who progresses.
Jose Anigo quit as coach of Tunisian club Esperance after Saturday's 0-1 home defeat by Al Ahly in Group A of the Confederation Cup.