Sinclair has started only three games since joining City last summer from Swansea for £6.2m and he was linked with a move back to South Wales earlier on Friday.
Mancini conceded he has not been able to give Sinclair many opportunities to shine and could understand if he was feeling frustrated as he spoke with the press ahead of the trip to play Swansea on Saturday.
"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."