Remove the door knob and latch mechanism.
Sand the damaged area, focusing on feathering down the edge between the old finish and the now unfinished areas. Start with an 80 grit and work in steps up to 120G or even 150G depending on how much you love this door. Be careful not to get too aggressive, this looks like a veneered hollow-core door and you want to leave some wood on there.
Clean the dust off the area. You can use a dry lint-free rag or tack cloth but don't get the unfinished part wet.
Get ready to refinish. I'd choose a water-borne polyurethane in a sheen that matched the existing finish, probably satin. Lay on a light coat with a good brush. Let it dry/cure. Lightly sand with a very fine grit sandpaper, clean and apply a second coat. Let it dry.
Re-install your latch and knob. Don't tell anyone about it and they'll never know.
PS: If you used regular masking (cream colored) or some other tape, try using blue masking next time. Also in hindsight you could have clamped wood on both sides and drilled a pilot hole through both so you could come at each side of the big hole from the finish side.
