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Sterling played centrally and netted a hat-trick, while striker Bony scored twice, in a 5-1 win over Bournemouth.
"We had to do something different," said Pellegrini. "With his movement we thought Raheem could be dangerous.
"He also missed three or four goals but he did very well."
Aguero, 27, is set to be out for a month with a hamstring problem while Silva, 29, is also likely to miss the Champions League visit of Sevilla on Wednesday and the first Manchester derby of the season against United at Old Trafford next Sunday (kick-off 14:05 GMT).
Sterling's first-half hat-trick was the first of his career, while Bony, who admitted he contracted malaria in pre-season, doubled his City goals tally since his £28m move from Swansea in January.
But Pellegrini said he was pleased with England international Sterling's finishing.
"I am happy because we changed Sterling's position and played him in the middle, with Bony in front of him," added Pellegrini.
"We felt it was better for him to be near Bony and also near the box.
"When we bought Raheem in the summer I said we are buying a 20-year-old who is very young and needs to improve. He is not a striker but he can improve his finishing and, today, he did."
Sterling, whose best scoring record was 11 goals with Liverpool last season, said he had been doing extra work on his finishing.
The £44m signing, who has now scored five goals in 11 City appearances, said: "In training I have been working on one-on-one situations in a few sessions.
"It is something I will keep working on and hopefully I will get better at it."
Bony also praised Sterling's performance after the Ivory Coast striker scored his first goals of the season.
"We talked a lot in training this week," the 26-year-old said. "I know he is very quick and I told him if I jump you have to run, there is no need to think about if I win the ball or not.
"When we have the ball I look to show myself, it worked today. I am happy about the result and happy he scored three goals."
City skipper Vincent Kompany remained on the bench against Bournemouth, with Pellegrini saying the defender was not yet ready to return despite playing for Belgium on Tuesday.
Belgium manager Marc Wilmots' decision to play Kompany angered Pellegrini after the 29-year-old picked up a calf injury against Juventus on 15 September.
But Pellegrini said his omission on Saturday was for fitness reasons only.
"We finished playing with Nicolas Otamendi and Eliaquim Mangala in the last game and they did very well," the City manager added.
"He was on the bench because he played for Belgium on Tuesday and couldn't work on Wednesday and Thursday. I think working just one day after one month injured is not enough to play again."

A group has called for a protest at Parliament on 8 October against legislation banning baring your buttocks.
The tongue-in-cheek event, scheduled one day after the full moon, calls for the right to bare bums.
Police said: "The only moon we want to see on Parliament House is the 8 day old moon in the October lunar cycle."
An amendment included in an overhaul of sexual offence laws specifically bans "mooning or streaking". First-time offenders face up to two months in jail while repeat offenders could spend six months behind bars.
Disgruntled mooners set up the protest as a Facebook event on Monday.
"Following the recent banning of the royal moon in Victoria, we have decided to show our [disgust] and [devastation] of this new law," the group said on social media.
However, Victoria Police responded asking the members to keep their pants firmly around their waist.
"We suggest keeping your pants on and shut this page down or potentially risk criminal charges," the Facebook post by Victoria Police read.
Manchester City boss Manuel Pellegrini praised Raheem Sterling's combination with Wilfried Bony as the pair proved able deputies for injured duo Sergio Aguero and David Silva.
[NEXT_CONCEPT]
Victoria Police have urged Australian mooning enthusiasts to keep their pants on or risk criminal charges.