Tunisia, ranked third in Africa, bowed out of the Cup of Nations after drawing 0-0 with South Africa in a poor final round Group E match in Korhogo on Wednesday.
The North Africans had a late chance to snatch victory and survive, but substitute Haythem Jouini headed a cross well over the crossbar.
Tunisia became the second top 10-ranked nation after Algeria to be eliminated after the opening round.
Mali won Group E after a 0-0 draw with Namibia, and both qualified for the knockout stage along with second-placed South Africa.
Tunisia dropped veteran captain and forward Youssef Msakni after he made little impact in a loss to Namibia and draw with Mali. Defender Yassine Meriah took over as skipper.
After a four-goal hammering of Namibia, South Africa retained the same starting line-up, which included eight players from Mamelodi Sundowns, the dominant domestic club.
The early stages were cagey and scrappy in the 36 degrees Celsius (97 Fahrenheit) heat of northern Ivory Coast, with Tunisia having more possession, but not using it effectively.
Tunisia squandered three half-chances midway through the half as Ellyes Skhiri blazed over, Anis Ben Slimane overhit a free-kick and Elias Achouri headed wide.
A strong run by Percy Tau for South Africa ended with Evidence Makgopa nodding wide and a speculative long-range shot from Thapelo Morena dipped just over the crossbar.
By the end of a disappointing half, Tunisia had five goal attempts, but not one on target in a match watched by Confederation of African Football (CAF) president Patrice Motsepe.
The start of the second half was delayed by several minutes so that the kick-off coincided with the other Group E match between Mali and Namibia in the southwestern coastal city of San Pedro.
As the hour mark approached, Qatar-based Msakni replaced Ben Slimane and won his 100th cap for the Carthage Eagles.
This month, Msakni became the fourth player after Cameroonian Rigobert Song, Egyptian Ahmed Hassan and Ghanaian Andre ‘Dede’ Ayew to feature in eight Cup of Nations tournaments.