Basic economics say that given a certain price, you get a certain demand. And if the price rises, then demand goes down. Consumers don't blindly pay more for things when their prices go up.
In basic microeconomics, taxes, market power, and other market distortions create deadweight loss. Again, the higher price is borne by the consumer, regardless where in the supply chain/production process it is injected. Higher costs can flow through without deadweight loss, but again this is all in the static scenario.