"Shucks!"

DRAT

This exclamation of frustration starts with a D and rhymes with "hat."

"Shucks!" is an exclamation of frustration, similar to "drat." The clue plays on the idea that both words express mild annoyance or disappointment. Since "drat" is a more concise and commonly used term in crosswords, it fits as the answer. The wordplay here is straightforward, relying on synonyms for a lighthearted tone.