Former Manchester United striker seen holding aloft the poster after Red Devils boss said that Roberto Mancini's side would not win the Premier League title 'in his lifetime'
The former Red Devils striker was given the poster by a fan at their trophy parade and was seen holding it aloft live on Sky Sports.
The poster was in retaliation to comments made by Ferguson previously in the season when he said that City would never win the title 'in his lifetime'.
A City spokesperson said: "The creation of the tasteless material is in itself reprehensible. In accepting and brandishing it, Carlos has made a significant error of judgement.
"The club wishes to express its sincerest apologies to Sir Alex Ferguson and Manchester United for any offence or distress caused."
Tevez has also apologised for the incident, claiming that he meant no disrespect to his former manager.
"I got carried away in the excitement of the moment and I certainly didn't mean any disrespect to Sir Alex Ferguson, who I admire as a man and a manager," Tevez said in a statement.