He also says the young forward must improve his finishing to do so despite a hat-trick at the weekend.
The youngster was in fine form as his side ended up as 5-1 winners on Saturday, scoring his first ever career hat-trick in a hugely impressive display.
However, he had several other big chances throughout the game to add further goals to his tally and will have been disappointed not to finish the game with more goals to his name.
And Pellegrini says he still has to improve his finishing, although he does think he will score more goals this season than he ever did at Liverpool.
“I think it was important for Raheem to score three goals,” he said to mcfc.co.uk
“He must improve his finishing – he did that today, he’s young and will continue to get better. I don’t think he’s a striker like Kun or Bony but this year, and I said it when he arrived, I am sure he will score more goals than he did in another season at Liverpool.”
Sterling was employed as an out and out striker against the Cherries, partnering Wilfried Bony up front in the absence of Sergio Aguero.
It was important he put in a big performance as well having been hauled off in the 6-1 victory over Newcastle United before the international break as a result of a poor performance.
And Pellegrini says it was important for him to put in a top performance, saying that putting him alongside Bony allowed him to have the space he needed to perform.
“He didn’t lose confidence because I spoke with him immediately after he came off,” he added.
“He didn’t play well but all of the players can have a bad day. It was important for him and the team to change his position today. I though that near Bony he could have a lot of space.”