City will take on Liverpool away from home at Anfield in the Premier League on Wednesday evening, and Sterling is likely to start.
Ahead of the match, Pellegrini said that he is backing the 21-year-old attacker to perform against his former club.
"Players that cannot play in a difficult environment are not top players,” the City boss told BBC Sport. "I have 100% trust in him.”
Former City forward Marsh has suggested on Twitter that Pellegrini should not have too much faith in Sterling.
>That's probably 70% too much trust... https://t.co/NajmX3UNYr— Rodney Marsh (@RodneyMarsh10) March 1, 2016
Sterling, who can play as a winger, attacking midfielder or striker, joined City from Premier League rivals Liverpool in the summer of 2015.
The England international has scored five goals and created 35 chances in 24 league appearances so far this season.
The youngster has a pass accuracy of 86% and a shot accuracy of 59%, and has won seven headers, 37 dribbles and 18 tackles.
City are fourth in the Premier League table at the moment with 47 points from 26 matches.