Pinnick along with four other Nigerian Football Federation officials are under investigation by a Nigerian court for corruption and financial embezzlement.
"As we make big decisions, it's scary for people on the outside but on the inside, we are convinced about the efficiency of this progression," CAF chief Ahmad Ahmad said during the body's executive committee meeting in Cairo.
"I reorganised my office so it becomes more efficient," he added.
Pinnick was replaced by Congolese official Constant Omari Selemani, who was formerly CAF's second vice-president, as Ahmad's number two.
Additionally CAF and FIFA signed on Thursday an agreement which will see expertise from the global body used to help assess the African confederation's current situation and speed up reforms plans aimed at ensuring the organisation operates with "transparency and efficiency".
FIFA secretary general Fatma Samoura was appointed general delegate for the continent for six months starting on August 1.
"We are experiencing a serious situation," Ahmad said.
"If I have a problem at home my questions are answered by my parents. Who should I go to when I have a big problem? For me, the mother house is FIFA."
The final of this year's Africa Cup of Nations takes place on Friday with Senegal facing Algeria in Cairo.