Prior to his sacking from City, Mancini took the blame in early May for winger Sinclair's lack of action following his £6.2million arrival from Swansea last summer.
Sinclair last started a Barclays Premier League game last September, following which he managed just 70 minutes of top-flight football for the club after being relegated to the bench.
Even before Manuel Pellegrini's arrival, Sinclair decided he had to leave the Etihad Stadium to discover the joy of playing regularly again, leading to the 24-year-old signing on a season-long loan deal with West Brom last week.
"It gets to the stage when you get a bit older and you see politics in football, which no-one (on the outside) sees," said Sinclair
"It's things like that, in the backroom, when he (Mancini) said he didn't give me a chance, which he didn't.
"I even asked him 'Why did you bring me in if you're not going to give me a chance? You've given me no game time to show what I'm about', and he couldn't really answer the question.
"As a player, if you're not getting a chance to play then you are going to see the manager and ask him what is needed.
"So I did see him a few times, and we had our differences, but that's football.
"Not being given an opportunity to play was frustrating, but that was the choice I made, I never kicked up a fuss. All I could do was put my head down and train every day."
It is the second time in Sinclair's career he has spent time at a big club, only to be starved of opportunities, as was initially the case at Chelsea from where he went on loan to six lower league sides prior to joining Swansea.
Sinclair concedes should another opportunity of a move to a high-profile club materialise again then he would not jump at it.
"People have asked me why I left Swansea to go Manchester City, but if I had stayed then people would have said I've no ambition, so this is the problem I had," added Sinclair.
"I made my decision to leave, and I don't regret it because in football sometimes those opportunities don't come around again.
"With three years left on my contract I could have stayed at City, not played or be bothered, but I'm hungry to play, which is why I have had so many loan deals.
"When I was at Chelsea I wasn't playing, which is why I went out on loan so many times because of my hunger to play.
"I now really hope I can settle (at West Brom) and have a great start from Sunday onwards, score some goals, help to win games and if I'm happy enough then hopefully I'll stay.
"But I definitely would think twice about doing it (moving to another big club) at this stage of my career."
After making his debut for the Baggies in Tuesday's 3-0 Capital One Cup win over Newport, Sinclair is now likely to face old club Swansea at The Hawthorns on Sunday.