。
She felt embarrassed about her failure.
Literal
She [topic-は] failed [and-して] embarrassed felt.
失敗して (having failed) chains via て-form into 恥ずかしく思った (felt embarrassed). 恥ずかしく思う uses the adverbial form of 恥ずかしい (embarrassing) with 思う (to feel/think) — a standard pattern for expressing how one feels about something. The failure is the cause; the embarrassment is the emotional response.