While City ended the season empty-handed, Mancini believes he deserved to stay for winning two trophies in the previous two years.
Instead, the club appointed Chilean coach Manuel Pellegrini, who takes charge of pre-season training for the first time on Monday.
Mancini said: "I lost the FA Cup, it can happen. It was a bad day for the whole team.
"But I never expected what happened, I never believed the rumours about Pellegrini were true.
"I still don't understand the reasons. I deserved more respect. City demanded I won the title within three years, I won it within two years.
"I'm not angry with the owner Mansour or the chairman Khaldoon Al Mubarak. They are two great managers and I'll always be grateful."
"In 3½ years my staff and I did an extraordinary job. We rebuilt a club that was not at the top level.
"They wanted Champions League, I got them there. We beat Manchester United 6-1 at Old Trafford. For three years City played the best football in the League."