Soft cry of pain produces purse but not of the lips (5)

I believe the answer is:

pouch

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'purse but not of the lips' is the definition.
I can't judge whether this definition defines the answer.

'soft cry of pain' is the wordplay.
'soft' becomes 'p' (musical abbreviation for piano, 'soft').
'cry of pain' becomes 'ouch' (exclamation said when in pain).
'p'+'ouch'='POUCH'

'produces' is the link.

Can you help me to learn more?

(Other definitions for pouch that I've seen before include "Marsupial's baby carrier" , "Kangaroo's pocket" , "Container for tobacco or young" , "Bag" , "joey's home" .)

I've seen this clue in The Globe and Mail.

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