。
She felt humiliated by his blunt words.
Literal
She [topic-は] his [genitive-の] blunt [adj-な] words [by-に] humiliation [object-を] felt.
に here marks the source/cause of the feeling — 'at, by, on account of.' おぼえる ('to feel, sense') is one of those verbs whose meaning shifts with what's marked as the felt thing: 屈辱を覚える ('feel humiliation'), 違和感を覚える ('feel out of place'), 寒さを覚える ('feel the cold'). In each case the felt sensation takes を, and what triggers the feeling takes に. 率直 ('frank, blunt') is positively framed in many contexts (率直な意見, 'frank opinion') but here cuts the other way — bluntness can wound.