Hi,
No, 'use' is not wrong here. In fact, it's commonly said in a context like this.
Your grammar book seems to be concerning itself with vocabulary and meaning rather than grammar.
In strictly grammatical terms, you just need a transitive verb.
In other words, a sentence like My pen is out of ink, may I eat yours? has a foolish meaning, but it is correct grammar. 
Best wishes, Clive