Producers almost never have the power to arbitrarily raise prices in response to increasing costs. Simply put, if it were possible for them to bring in more revenue by setting a higher price they would already have done so.
However, rising costs do have one noticeable *indirect* effect on prices: under some conditions they can nullify the profit margins of the marginal producers, thus forcing them to go out of business and reducing the overall supply of the good. At that point prices must rise such that supply and demand regain their balance. However, the change in price is typically less than the change in cost, so the rising cost is born in part by both the producers and the consumers, not simply "passed on".