Pellegrini feels the 20-year-old forward, whose finishing ability has been criticised, has been working hard to improve his game since his £49m (70m) summer move from Liverpool.
Sterling was on target for the sixth time this season with the opening goal in Tuesday’s Champions League win at Sevilla.
The England international’s best tally in a season is the 11 he scored for Liverpool last term but Pellegrini thinks he should surpass that.
Pellegrini said: “I know he scored 11 for Liverpool and I don’t think that’s a huge amount for Raheem. He must score more and to do that he must work a lot.
“But he soon settled into our style of play and I’m happy that he has six already.
“It depends on how many games they are playing in, but of course Raheem is a young player and I was sure from the beginning that he must improve a lot.
“When you are 20 years old and you work as a good professional you must improve. Playing every day with important players is good for a young player, you are always learning from experienced players.
“And the next thing, which is very important, is that the style we play is good for him. He will have good chances to score. Now we must be quiet and let him do it in the correct way.”
City face basement club Aston Villa this weekend but Pellegrini expects a tough test from a side now managed by Remi Garde.
He said: “I don’t know who said it was going to be easy. For me there are no easy games in the Premier League.
“They are at the bottom of the table with a new manager so the motivation to try not to be relegated will be high.”