How to resurface a patch of hardwood floor? Reapplying stain and poly
You need to treat the touchup in only those three rows affected, working with the grain. You need to sand out, way farther then the affected areas. The area to be repaired will, ideally, be the entire three rows. You should, at least taper the damaged area way way out. Feather it out far, so the stain won't have such a hard line. If that's oil based stain, make sure to wipe the affected area down with paint thinner, really get in there and scrub it out. Keep scrubbing and rinsing until the rag comes up clean.

On the retouchup itself, use a quality china bristle brush, lay the stain on thick. You're just going to have to experiment with how long to let it lay before you wipe it off.

You will always see your repair, for the rest of your life. Your goal needs to be "not as noticeable", rather than "never happened". Sorry about that, but that's the way it is. The job you're tackling is difficult for those of us that do this for a living, let alone someone who does it once or twice in their life.