My immediate instinct is to switch subject and object. Though I'd be happy to learn that there is a Latin way of saying "X fits in Y," there are definitely natural ways to say "Y holds X." My suggestion for "The souvenir does not fit in my bag" is:
Sacculus non capit monumentum.
(Thanks to Tony in the comments and Tom Cotton's answer for their suggestions on how to translate "bag" and "souvenir.")
Here's a similar example from Seneca the Younger:
nam magna non capit exigua mens. (Controversiae, 2.1.13)
For a small mind can't hold big [ideas].
Big [ideas] don't fit in a small mind.