Bony has had mixed success as he leads the line in the absence of Sergio Aguero, who injured his hamstring on international duty with Argentina at the start of October.
The Ivory Coast striker has scored three times in five games but has often attracted groans of disapproval from the Etihad crowd, not least against Norwich City on Saturday as he missed a string of chances.
But Pellegrini admits that while the former Swansea City man needs to find the back of the net, fans should play their part in helping him back to form.
"Maybe he needs to score, because he is missing some chances," Pellegrini told reporters. "The way he plays and the striker he is, he normally doesn’t miss them."
Bony has endured a stop-start career at City since joining the club in January, and missed much of pre-season with Malaria.
“I think he needs trust," Pellegrini added. "He is playing after many months of not being able to work normally, for different reasons. Now I have placed a lot of trust in him, he must demonstrate why he’s here.”
“Not only patient. I think we must support him, because he is an important player," explained.
"He must play with Kun, without Kun. He makes a lot of space, he holds the ball up well to create space.
“And unfortunately at this moment, as happens with a lot of strikers, he’s not scoring the number of goals that he can.
“But I am sure that in the future, he will return to his normal performance.”