The 24-year-old has started just three games for City since his £6.2million move from Swansea last August.
"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."
Sinclair has been linked with a return to Swansea ahead of City's Barclays Premier League trip to the Liberty Stadium this weekend.
Mancini accepts he has not given the Great Britain Olympic player much opportunity and could understand if he was frustrated.
When asked if that might mean Sinclair deserves to play somewhere else, Mancini, speaking at his regular press conference, said: "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."
- Sports & Recreation