City face Sinclair's former club Swansea City this weekend.
"This situation with Sinclair is difficult because I didn't give him a lot of chances to play. He is very unlucky," Mancini said.
"It is my fault, not his fault. A young player like Scott who is a good player deserves to play always. For him, it was a really difficult year this year.
"Scott is young and he has good quality but this year was difficult for him. I think it is better if he can have another solution.
"If he stays here, maybe, everything can change but I can understand his frustration in this moment because he didn't play a lot of games.
"For me, he is a good player. We have one team. For him, it was difficult. I repeat - he did everything well, he worked well, he is a good guy, he deserves to play. I can understand when one player can't play often it is difficult."