Not all holes can be patched. And you could get multiple flats if you fail to remove what caused the first flat or just get unlucky. I always carry both a tube and patches, and a pump and CO2. Also a small piece of Tyvek as a temporary boot in the event of a larger hole in the tire. You'll either learn this through experience or by listening to others.

The "walk of shame" can be long and lonely, but is a great motivator. I did it only one time, when my spare tube had a hole, I carried only a single CO2 cartridge, and was several miles from civilization. It takes a long time to push a bike that distance. Never again.