Referee Rajindraparsad Seechurn gave Equatorial Guinea a controversial penalty in stoppage time as they beat Tunisia 2-1 in the quarter-finals.
Tunisia staff confronted the official after the match and their federation has been fined $50,000 (£33,000).
"The referees committee noted the poor performance of the referee," the Confederation of African Football said.
Caf added that the referee's failings included an "unacceptable failure to maintain calm and ensure proper control of the players during the match".
Caf also wants an apology from Tunisia for accusations of bias.
And Tunisia have been ordered to pay for damages to a door and a refrigerator in the team's dressing room at Bata Stadium.
Mauritian referee Seechurn awarded the penalty in stoppage time after Ali Maaloul was harshly ruled to have fouled Ivan Bolado when Tunisia were leading 1-0 and, after equalising from the spot through Javier Balboa, hosts Equatorial Guinea went on to win in extra-time.
Seechurn has also been removed from Caf's list of elite referees.
According to Caf, it was sent two letters by the Tunisian FA following the match, with the second asking for an investigation and suggesting that Caf and its officials "were questionable and biased against Tunisia in general".
Unless Tunisia's football federation can provide "irrefutable evidence to substantiate the accusations" they need to send a letter of apology by midnight on 5 February or face expulsion from the 2017 Africa Cup of Nations.
Tunisia football chief Wadie Jary resigned from Caf in protest after the match and he was also "condemned" for his behaviour after going on to the pitch to confront Seechurn, as well as criticising the referee and African football's governing body.
Equatorial Guinea were fined $5,000 (£3,300) for poor security at the stadium.

Electronics giant Sony, as well as automakers Honda and Toyota cited damage at their plants.
The quakes killed at least 41 people and have caused severe destruction to buildings and infrastructure.
The suspensions in Kumamoto, a manufacturing hub, could cause supply chain disruptions.
Chipmaker Renesas Electronics also said there had been damage to some equipment at its Kumamoto plant, which produces micro-controller chips for cars.
Toyota said it would suspend operations at most assembly plants across Japan. The suspension across Toyota's facilities will be done in stages, and will last for about a week.
The world's biggest car manufacturer said it had been unable to source parts from some of its suppliers. This includes its affiliate Aisin Seiki which is a key supplier for Toyota.
Japan's Nikkei newspaper has reported that Aisin Seiki has been forced to stop producing doors, engines and other parts at its subsidiary in the Kumamoto prefecture, as the area is still experiencing aftershocks. The company is making plans to shift production to other facilities at home and abroad.
The staggered suspension across Toyota's plants is expected to lead to a drop in production, by about 50,000 vehicles, the Nikkei said citing industry analysts.
Sony said at the weekend it was assessing damage at its factory producing image sensors for smartphones, and that the plant would remain closed.
The earthquake in Kumamoto has also affected restaurants and retailers in the area. Supermarket operator Aeon kept all 27 stores in the area shut on Sunday.
An Africa Cup of Nations referee has been banned for six months for "poor performance".
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A number of Japanese manufacturers have suspended operations after two powerful earthquakes hit Kumamoto in south-western Japan.