Benteke is currently out with a knee injury, with the Belgian international undergoing minor surgery earlier this week to try and solve the troublesome problem.
Eagles boss Roy Hodgson confirmed earlier this week that he expects the 27-year-old to be out until the new year.
But Parish said that while he hopes Benteke will come back sooner, he says his absence provides an opportunity for Jordan Ayew.
Ayew is yet to score a goal for Palace after five Premier League appearances.
“You will get them [injuries], and other people have got to take their chance," he said.
“Christian [Benteke] will come back, and hopefully he might come back sooner, and we are hopeful that with a fair wind we might get him back before January.
“These things aren’t always an exact science, timing wise, so we are hopeful that we may get him back sooner, and of course we have Connor [Wickham], who came back against Dulwich, and Alex [Sorloth] and Jordan [Ayew], so we have got other players who have got to step up and take their chance."
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