The 24-year-old looked set to flourish at City after a promising season with Swansea but found first-team opportunities hard to come by as he made only 11 league appearances last term.
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Sinclair left City earlier this month after signing a season-long loan deal with West Brom with a view to a permanent deal.
"I never got a consistent run of games at Manchester City and I believe I could have been a success if the manager had given me a chance," he said.
"I went to see Mancini and asked him ‘why did you bring me in if you’re not going to give me the chance?' - but he couldn’t answer the question.
"I said to him ‘You’ve given me no opportunity and no game time. Why am I here?’. As any player, if you’re not getting your chance, then you’ve got to see the manager. You have to ask how you’re going to get your chance.
"I went to see him a few times and we had our differences. It does frustrate you when you don’t get that opportunity and build up to nothing.
“It’ll make me think twice about joining a club like that at this stage in my career. When the new manager [Manuel Pellegrini] came in I'd already made my mind up to leave."
Sinclair is in line to make his West Brom debut on Sunday against former club Swansea at The Hawthorns.