With the scores level at 0-0 in the 93rd minute, Everton defender John Stones made contact on Sterling with a sliding tackle near the goalline in the dying seconds.
Pellegrini threw his arms out in frustration when referee Roger East, who appeared to have an unobstructed view of the incident, did not point to the spot.
"Everyone in the stadium could see it was a penalty, it was so near to the referee and so clear,” Pellegrini told the BBC.
"Both Raheem’s legs were taken by Stones but if he doesn’t whistle we can’t say anything."
Everton boss Roberto Martinez had a different take on the incident.
"John Stones goes to slide to block the ball, Raheem Sterling does not play the ball and waited," Martinez said.
"In my eyes it is an area that is not certain if penalty or not. I believe the referee should control their emotions and the referee did exactly that. It is impossible to be 100 percent certain and I am pleased he did this and showed his maturity."
City’s failure to score at home in a Premier League game for the first time this season cost them two points and left them three points behind leaders Arsenal and Leicester City.
After a mediocre first half, City dominated the second, but the Everton defence held firm.
“Maybe first half it was close, but we played well in the second half,” Pellegrini said.
“I think we were the better team, Everton didn't create any chances, we had 17 shots but for different reasons we didn't score."
(Reporting by Andrew Both in Cary, North Carolina, editing by Ed Osmond)
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