You can (and should) use a structural patch, such as you can get for auto tires at a parts store; they are both thicker, and fabric reinforced. Depending on the location of the damage, you'll likely feel a thump when it passes the ground. If the damage is close to a bead, you should abandon the tire, as that area is highly stressed.
While you CAN repair a tire that has been damaged as such, they are typically viewed as temporary repairs until the tire can be replaced altogether. For a bike that is used as transportation (I'm guessing?) such a repair is a liability...it will break when most inconvenient, so you might as well replace it with another tire.
BTW, a bike rolled on the rear wheel is quite a bit more maneuverable than one rolled as if it was being ridden--I've encountered very few spaces where I couldn't get a bike through. Just some food for thought.