The winger was signed from Swansea City in the summer and the former Chelsea man says that it was the day he put pen to paper on his contract that made him realise that he had joined one of the world's biggest clubs.
"It really hit me that I'd joined the champions when I signed my contract at the Etihad Stadium and it flashed on the screens that we'd drawn Real Madrid in the Champions League," said Sinclair.
"This is why I came here, to play with the best and be in a world-class team and, as a result, develop into a better player.
"I really enjoyed my time at Swansea and was playing regularly from the word go but I just felt the time was right to move on."
Sinclair has found his first-team opportunities limited at the Etihad Stadium this season.