Crossword Genius

Felt sad about a good cinema that's shabby … (7)

Ross

I believe the answer is:

fleapit

I'm a little stuck... Click here to teach me more about this clue!

'cinema that's shabby' is the definition.
I can't tell whether this defines the answer.

'felt sad about a good' is the wordplay.
'sad' is an anagram indicator.
'about' means one lot of letters goes inside another.
'good' becomes 'pi' (I've seen this in other clues).
'felt' is an anagram of 'flet'.
'a'+'pi'='api'
'flet' going around 'api' is 'FLEAPIT'.

Can you help me to learn more?

(Other definitions for fleapit that I've seen before include "Scruffy cinema" , "Run-down place for pictures" , "Shabby place" , "jumper" , "shabby public building" .)

I've seen this clue in The Guardian.
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