Our fertilizer pouches alone will be a deterrent for moss, but they shouldn't be considered a knockout punch.
Our Dandelion Doom is a selective herbicide that eliminates moss and will not hurt your grass.
For more long term control, make the area less habitable for moss. Moss loves shade and acidity; try allowing more sunlight in by pruning some branches (your grass will love the extra sun!) To raise the pH, annual lime applications will help. Keep in mind that it takes a ton of lime to move the pH scale; don't be surprised if results aren't noticeable on soil test results.
For larger areas, bring in some shade blend grass seed where the moss used to be. This will look better sooner, and help prevent the moss from coming back.
We now offer a Shade Blend grass seed for those hard to grow areas. Currently this works best in Northern and Northern Transitional zones. This blend has 4 types of grass seed. It grows well in medium to high shade conditions. It is a lower maintenance grass seed blend that requires less sun and fewer nutrient inputs to thrive. It's sold in a 5lb bag for $39 and can be purchased on your account page for current customers.