Embarrassed about being dismissed, or beaten (6)
I believe the answer is:
routed
'beaten' is the definition.
(synonyms)
'embarrassed about being dismissed' is the wordplay.
'embarrassed' becomes 'red' (someone may blush or go red when embarrassed).
'about' is an insertion indicator.
'being dismissed' becomes 'out' (in cricket, to be out is to be dismissed).
'red' placed around 'out' is 'ROUTED'.
'or' acts as a link.
(Other definitions for routed that I've seen before include "brought to light" , "Put to flight, scattered" , "Sent in particular direction by way of detour" , "Sent (along a specified course)" , "Vanquished" .)