Greek character upset by my lacking manners (10)

'lacking manners' is the definition.
(ungracious means impolite)

'greek character upset by my' is the wordplay.
'greek character upset' becomes 'un' (I can't justify this - if you can you should believe this answer much more).
'by' says to put letters next to each other.
'my' becomes 'gracious' (both are exclamations of surprise).
'un'+'gracious'='UNGRACIOUS'