Accepting defeat finally, was first to admit disappointment (7)

'disappointment' is the definition.
(something or someone which lets you down)

'accepting defeat finally was first to admit' is the wordplay.
'accepting' indicates putting letters inside (inserted letters are accepted).
'finally' suggests the final letters.
'was first' becomes 'led' (to lead is to go first).
'to admit' becomes 'own' (own can mean to admit or acknowledge).
The last letter of 'defeat' is 't'.
't' going inside 'led' is 'letd'.
'letd'+'own'='LETDOWN'