Ivory Coast striker Bony had scored three in four games while City's star forward Sergio Aguero was out with a heel injury.
But Aguero was back for Monday's clash at the Emirates Stadium and started as City lost 2-1 in a match that could have a significant bearing on the title race.
With City boss Pellegrini's position already under increased speculation following Pep Guardiola's announcement he will be leaving Bayern Munich next year, Bony has heaped more pressure on the Chilean with his rant.
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When asked by reporters if he deserved to be starting instead of coming off the bench in the second half, Bony said: "I think so.
"He (Aguero) is coming back from injury. He hasn't played for a couple of weeks. I'm disappointed today that I didn't start but I'm not the coach.
"The coach does what he thinks is best for the team. I'm sure everyone on the bench wants to play. He just has to choose 11 players.
"So when I come on I just try to do my best to try to score or to give an assist to the other players to score to help the team to win."
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Bony, 27, arrived at City from Swansea in January for a fee of £28 million ($41.5 million; 37.9 million euros) but has only started 10 league games in that time.
He also revealed he would talk to Pellegrini about his position amid speculation regarding his own future.
"That's my feeling today," he said when asked if he would air his views to his manager.
"We have lost the game so we just have to be ready for the next game. I will continue to work hard and think about the next game, prepare very well then it will depend on the coach who he is going to put in."
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