Sterling, who joined City last week in a £49m deal, impressed during the first 45 minutes of the 2-2 draw, scoring with just 137 seconds on the clock after latching onto Kelechi Iheanacho’s pass.
The England international continued to give Roma full-back Alessandro Florenzi a torrid time at the Melbourne Cricket Ground before being taken off at the break.
And City boss Pellegrini was impressed with his performance, claiming he can only improve playing alongside the calibre of his new team-mates at the Etihad.
“I think for a striker it’s always important to score, especially when he scored early in the game,” he said.
“He played just 45 minutes and has only worked with our team for a few days so I’m happy in the way he played. He demonstrated why he’s here.
“He’s a very young player so I think he’ll improve a lot in the future, playing with Yaya Toure, David Silva and Sergio Aguero. I’m very happy for him. I’m very happy for our team to buy him.”
Sterling also showed promising signs in partnership with Silva, and Pellegrini believes the former Liverpool forward will benefit playing in front of City’s current crop of midfielders.
“Good players always link immediately when they know how to play,” he said. “Immediately, David found a very good striker making good movements.
“At the moment, I think we have the complete midfield. We have very technical players. I think he will benefit from that so I am very happy about the future I think we’re going to have as a team.”