Clean the surface of the patio by sweeping away any loose dirt or debris with a broom. Clear off ingrained dirt or stains with a pH-neutral cleanser and a mop.
Chip away any loose or jagged concrete from the nicked area with a chisel and hammer. Place the tip of the chisel at the base of the jagged piece where it connects to the undamaged portion of the patio slab and strike the head of the chisel with the hammer to cut the piece away. Sweep all chips from the surface with a broom before continuing with repairs.
Place a strip of masking tape along the borders of the undamaged patio surrounding the nicked area to prevent the spread of the patching material over the good surface areas. Build a form made of 2-by-4 planks along the edge of the patio surface if the nick is located along the edge. Place the wood flat against the edge of the concrete and then secure it in position by planting wooden stakes into the ground along the rear using the hammer to drive the stakes into the soil. Use two planks to create corner pieces, securing the two planks together with wood screws.
Brush acrylic bonding agent over the damaged area with a paintbrush. Wait for the bonding agent to dry enough to lose its wet appearance, but remain sticky when touched. The bonding agent helps the repair material adhere to the old concrete, preventing it from cracking off due to slab movement.
Mix a small batch of quick-set concrete in a bucket using an electric drill with a paddle bit attached. Follow the manufacturer's instructions for the amount of water needed to create the patching material.
Spread the concrete over the nicked area, filling the missing concrete with the quick-set using a steel trowel. Smooth the surface of the patch with the trowel so that it's even with the rest of the patio slab. Wait overnight for the patch to cure.
Remove the masking tape and wooden form if used. Brush concrete sealer over the entire patio to protect the new patch as well as the old concrete from staining.