Pull the nail out of the brick with a clawed hammer. For stubborn nails, drill into the brick on either side of the nail with a masonry bit to loosen the nail and widen the hole before pulling out the nail.
Combine the mortar mix with water in a disposable cup. Use the water-to-mortar ratio recommended on the package. Properly mixed mortar is thick but fluid enough to apply easily, with a consistency similar to oatmeal.
Sprinkle brick dust into the mortar. Mix the dust in with a paint stirrer. Continue adding dust until the mortar looks similar in color to the existing brick.
Force the mortar into the nail hole with a putty knife. Smooth the surface of the mortar by scraping the excess away with the knife.
Rub the mortar with a coarse-texture rag once the mortar has set but before it dries completely. Use the rag to create a texture in the filler similar to that of the surrounding brick.