棚 and 引き出し: shelves and drawers
Distinguish where items are placed from where they are taken out.
Putting items on a shelf
棚 (たな) means shelf. 「棚に本を並べました」 says books were arranged on a shelf.
「棚の上の箱を取ってください」 requests the box on the shelf. The location connected by の identifies which box.
Items inside a drawer
引き出し (ひきだし) means a drawer in furniture. 「引き出しに鍵を入れました」 means putting a key in the drawer.
「引き出しから鍵を出しました」 means taking the key out of the drawer. に and から mark opposite movement directions.
The scope of a search
「棚にはありませんが、引き出しにあります」 says the item is not on the shelf but is in the drawer. It does not deny the item's existence.
「上の引き出しだけ開けてください」 requests opening only the upper drawer. だけ limits which drawer to open.
Does 「棚にはありませんが、引き出しにあります」 report a lost item?
Show the answer and why
No. It gives the location: not on the shelf, but in the drawer.