The £30million signing from Shakhtar Donetsk made his first outing in a City shirt in Sunday's 2-0 friendly defeat to SuperSport United in Pretoria.
Fernandinho is enjoying getting to know Pellegrini, with the Chilean boss another new arrival at the club this summer.
"The players are already getting used to his style on and off the pitch," the 28-year-old told the club's official website.
"Pre-season is a good time for this. We can learn his personality.
"I'm enjoying working with him, but I think it will always take more time for the players and the manager to get used to each other fully.
"It seems like he has that real winning mentality and a strong football philosophy that he will make the players understand."
The Brazil international is expecting to see more match action in Thursday's clash with AmaZulu in Durban, with City then flying on to the Barclays Asia Trophy tournament in Hong Kong.
Building his fitness is his main target, but the experience of pulling on the City shirt is also exciting him.
"It felt like a great honour to play with such big names and fantastic players," added Fernandinho.
"I don't feel 100% fit yet but I have two weeks of pre-season now to train, then hopefully I will feel top quality."