Looks like you broke through the veneer / luan? Not sure from your pictures, but can you access the back side of that damage?
If so, I think I'd paint the back with wood glue then paint the front with Old English scratch cover for dark woods.
Filler and stain won't match the woodgrain pattern.
OR if you do want to try to match the stain, pull out a drawer that is the same shade and take it with you to the hardware store.
Family of five camping in a Spankin' new
Grey Wolf 26DBH LTD pushing a
'03 Dodge Ram 1500 via
10k/1k HaulMaster WDH stopped by a
Prodigy P2 brake controller