City's £32.5million striker suffered the indignity of being taken off with half-an-hour left in a 2-0 defeat at Everton last weekend, after himself coming on as a substitute.
Robinho told the Mirror: "I don't have a problem with Mancini. It's normal for a player to want to play but the coach makes the decision and I accept it.
"I've spoken with Mancini. I know what he expects from me and I'll work hard to do that for the team.
"I'm a professional, I'm dedicated and I always give everything in training. It's untrue to say otherwise.
"I want to be successful at City, I don't want to leave. I want to win things here and that's why I left Real Madrid for this challenge.
"What happened against Everton was rare. It's rare for any player to be substituted after coming on. But again, it was for the team.
"I don't think my World Cup place is at risk. The Brazil coach, Dunga, knows what I'm capable of and has confidence in me."