Sinclair made his Champions League debut for the club in the 1-0 defeat at Borussia Dortmund on Tuesday.
It was only the former Chelsea man's sixth appearance in all competitions since joining from Swansea City on transfer deadline day.
The 23-year-old says he was all too aware that there would be competition for places among Roberto Mancini's expensively assembled squad when he made the move north in August.
He insists he is determined to work hard in training, bide his time, and be ready to stake his claim when opportunities arise.
"It was great that I started the game [in Dortmund] for my experience in the Champions League, but I'm disappointed we lost the game" Sinclair told the club's official website.
"It's always going to need patience. I'm playing in a great side and I've got to be patient.
"I've got to take every training session as it comes and when I get the chance I've got to prove myself."