I shouldn't have done that first degree (3)
I believe the answer is:
doh
'i shouldn't' is the definition.
The definition suggests a singular noun which matches the answer.
'done that first degree' is the wordplay.
'that first' suggests taking the first letters.
'degree' becomes 'oh' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The first letter of 'done' is 'd'.
'd'+'oh'='DOH'
'have' acts as a link.
Can you help me to learn more?
(Other definitions for doh that I've seen before include "an exclamation from someone who's annoyed with himself" , "First note of tonic sol-fa scale" , "It begins the tonic solfa" , "First note of major scale in music" , "whoops!" .)