Mix a small batch of concrete according to the manufacturer's directions. Apply the concrete to any holes or cracks, using a trowel or putty knife. Let the concrete in the repaired areas set completely.
Put on a pair of safety glasses. Smooth the high spots with a grinder after the concrete has cured, creating a level surface.
Spread the indoor-outdoor carpet adhesive on the treads and molded edges of the concrete steps, using a notched spreader.
Align the edge of the rolled carpet with the back and one side of the top step. Unroll the carpet over the adhesive. Smooth out the carpet with your hands. Work from the center of the step to the edges to remove any air bubbles under the carpet.
Fold the carpet over the molded front edge of the step. Trim the carpet even with the bottom of the molded edge, using the utility knife. Press the carpet into the adhesive on the molded edge on the front of the step.
Trim the carpet to the width of the step's tread, if necessary, using the utility knife and straightedge. Clean any stray adhesive from the steps with adhesive solvent on a rag.
Repeat the carpet installation process for each step.