The sediment filter includes a generally three-sided pocket having one or more mesh screens forming the bottom and/or side surfaces for filtering sediment or other particulate in a brewed beverage being dispensed from a coffee brewer or the like. The filter selectively attaches to a portion of the carafe such as the lid or upper open rim and is positioned to filter brewed beverage flowing through an inlet port or passageway into the carafe reservoir. The mesh screens permit flow-through of the brewed beverage while simultaneously trapping or capturing suspended particles therein.