This is a fungus called black spot. Left untreated, it can cause all the leaves on your roses to turn yellow and fall off. It will also affect nearby plants, as it spreads by spores. Remove ALL INFECTED material and throw it away or burn it. Do NOT leave it on the ground as this fungus is very hardy. It can survive winter and travels very easily, even after being removed from the affected plant. Spray your plants regularly (bi-weekly) in the growing season with a good fungicide (I like the Bayer products). You can also add a little bit of dish soap and baking soda to a spray bottle with water and spray the entire plant.
Cover the cutting loosely, pot and all, with a plastic bag or plastic wrap and keep the soil moist. Putting a tall stake into the pot will hold the plastic away from the leaves. If the plastic touches the leaves, they remain wet and can succumb to a fungus disease. Along the same lines, make sure the condensation can escape from the plastic or the stem will rot.
Fertilizer: Roses are heavy feeders, and will benefit from a steady supply of nitrogen, phosphorus and potassium. You can provide these nutrients with either liquid or granular fertilizers, at a ratio of approximately 5-8-5. In most cases, regular applications of compost, rotted manure, fish emulsion and seaweed extracts will provide roses with all the nutrients they need. These organic amendments also help to moderate pH imbalances and stimulate beneficial soil life. Other organic amendments favored by rose growers include greensand, black rock phosphate and alfalfa meal.