Put off, I publicly talk rot (11)

I believe the answer is:

deteriorate

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'talk rot' is the definition.
'deteriorate' can be an answer for 'rot' (thesaurus). I am unsure of the 'talk' bit.

'put off i publicly' is the wordplay.
'put off' becomes 'deter' (both can mean to discourage).
'publicly' becomes 'orate' (I can't justify this - if you can you should believe this answer much more).
'deter'+'i'+'orate'='DETERIORATE'

Can you help me to learn more?

(Other definitions for deteriorate that I've seen before include "Get worse" , "Slip" , "Become slowly worse" , "Go downhill" , "Grow worse" .)

I've seen this clue in The Times.

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