Lose fight admitting that was painful (3,3)
I believe the answer is:
bow out
'lose' is the definition.
(as in bowing out of a competition)
'fight admitting that was painful' is the wordplay.
'fight' becomes 'bout' (as in a bout in boxing).
'admitting' means one lot of letters goes inside another (admit can mean to welcome in or accept).
'that was painful' becomes 'ow' (expression of pain).
'bout' enclosing 'ow' is 'BOW OUT'.
(Other definitions for bow out that I've seen before include "What a string player often gets" , "Retire from the scene with bodily gesture of acknowledgement?" , "Exit; retire" , "Withdraw from a situation" , "Retire gracefully" .)