Sinclair signed for City in a reported eight million pound move on transfer deadline day in August but has since gone on to start just two games for the club.
The winger netted eight goals in 38 games for newly promoted Swansea in the 2011-12 season and Mancini believes Sinclair is good enough to play for City, but should look to leave for the good of his career.
The Italian said: "Scott is young and he has good quality, but it was difficult for him this year. 
"I think that it would be better if he could find another solution, because if he stays here maybe I can change how I feel but I can understand his frustration at the moment because he hasn't played a lot of games.
"I don't know because this situation with Sinclair is difficult because I didn't give him a lot of chances to play and I think that it is also difficult for him. 
"It is not his fault - it is my fault. I think Scott is a good player and he deserves to play. So it was always difficult for him this year."
With Sinclair possibly on his way out, City have been linked with a move for Shakhtar Donetsk midfielder Fernandinho.
The Brazilian has impressed many this season with his dynamic displays, racking up nine assists from 34 games, but Mancini conceded chasing the player's signature would be tough.
He added: "I don't know. We can talk about Fernandinho, he is a good player. He plays for Shakhtar and is like all the other good players. 
"I don't think like there are a lot of good players around the world [that City could get] because there are four or five top teams who buy good players and this will make it difficult."
Mancini's side take on Swansea at the Liberty Stadium on Saturday and the 48-year-old is eyeing a win that would go a long way to guaranteeing second spot in the league and enable the Italia to give the lesser-used members of his squad a chance to impress in their last few games.
"Tomorrow is important for us, to win against Swansea, and we know it will be difficult," he said. 
"But if we win tomorrow we will get the chance to play our young players and also players that play for the second team, maybe, for the last two games. It is also important for us for the future."