They made the allegations after conceding a controversial stoppage-time penalty in a 2-1 defeat by Equatorial Guinea in the quarter-finals.
The game's referee has been banned for six months for "poor performance".
Tunisia had until Thursday to say sorry or face a ban from the 2017 edition.
After a meeting on Wednesday, the Tunisian FA refused to apologise with a spokesman saying the team had "suffered scandalous injustice from referees".
Caf, which fined Tunisia after players confronted referee Rajindraparsad Seechurn after the final whistle, had wanted the 2004 champions to apologise for "insinuations of bias and lack of ethics against Caf and its officials, or to present irrefutable evidence to substantiate the accusations".
African football's governing body said it had been sent two letters by the Tunisian FA after the match, with the second asking for an investigation and suggesting Caf and its officials "were questionable and biased against Tunisia in general".
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