This sentence is in my JLPT textbook:
つい舌{した}がすべってしまい、うそがばれてしまった。
I thought that it meant something like, "with an unintentional slip of the tongue, my lie was exposed." However, the sentence is marked as being an incorrect usage of すべる, and it doesn't explain why.
I know that one can say つい口{くち}がすべる, which in English I would equate with "a slip of the tongue," to accidentally say something one didn't intend to say.
In Japanese, is it only mouths that slip, not tongues?
(A helpful answer would not only confirm this with a yes or no, but ideally offer a little insight on how 口{くち} and 舌{した} differ in metaphorical terms.)