The Italian's departure from the club by mutual consent was confirmed on Wednesday and the former Inter and Manchester City boss claims that he left the club due to a dispute over their future direction.
"The targets were changed from those set in October when I arrived so, by mutual agreement, we decided to terminate our relationship," the 49-year-old told Sky Sport Italia.
"We had a good relationship for those eight months. I had a great time in Instanbul."
The Italian also backed 36-year-old Didier Drogba, who has confirmed that he will also leave the club, to have a big impact wherever the Ivorian decides to play his football next season.
"Drogba is a great guy and can make the difference, if not for 50 games," said the ex-City manager.
"I don't know if Juventus or any other teams are interested in him but, for 20-25 games, he can still make the difference. Time catches up with everyone but he can still be useful."
Mancini claimed the Turkish Cup and finished the league campaign as runners-up to Fenerbahce during his short stay with the club and has been linked with a return to former sides Sampdoria and Lazio.