The nails on a tack strip are also concrete acceptable. Do the same as if it was wood. Is your concrete flooring sealed? Do you have any condensation on the concrete floor that you have noticed in the past?
you need to practice with the tack strips on concrete. Take a scrap piece and get the hang of it. On concrete, you whap the nail once and only once to seat it in concrete. Repeatedly hits only make the fasten come loose. One well directional hard hit will do each nail.