The proper water supply to your pressure washer is of critical importance.  Most pumps do not need a pressurized feed but do need adequate flow of water to the pump.

For a pressurized system the flow from the source should be a minimum of 1.25 times the rating of the pressure washer. Any less may case serious damage to your pump.  

For a gravity feed system the flow should be no less than 1.5 times the rating of your pump. With gravity feed the inlet of the pump needs to be below the outlet of the source.  Most pumps will continue to draw water if the level of the source gets below the level of the pump inlet but only as long as the unit is running. This is a risky practice and is not recommended.  Once the pump is shut off it will likely loose it's prime and will cavitate causing serious damage. 

Some pumps will draw water from a source lower that the inlet of the pump.   

Also, just because you have adequate flow from your source does not necessarily mean you have adequate flow at the pump.  The style and size of hose or pipe that takes the water from the source to the pump is important.  Always have an adequate hose or pipe size to give you the flow you need at the pump.  Higher pressure will also give you higher flow through the same size hose or pipe.  If in doubt ask your pressure washer or hose supplier.