A great many lost out (4)
I believe the answer is:
lots
'a great many' is the definition.
(many examples of something)
'lost out' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'lost' anagrammed gives 'LOTS'.
(Other definitions for lots that I've seen before include "Oodles" , "may be drawn" , "Large number or amount" , "Many found in slot" , "Items offered at auction" .)