Sinclair, who moved from Swansea City last August, has only managed 14 appearances in all competitions for Manchester City this term and has yet to score a goal for Mancini's side.
Mancini maintains that the 24-year-old "deserves to play" but concedes he may not get a regular role at the Etihad Stadium.
"This situation with Sinclair is difficult because I didn't give him a lot of chances to play. He is very unlucky," said Mancini at his pre-match press conference.
"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."
When asked if that meant Sinclair would be moving on in the summer, Mancini replied: "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."