Austin netted a stunning 25-yard drive into the top corner three minutes before half-time, marking their first win in seven attempts.
Having only won four Championship games at home this season, Dyche was ecstatic with the result.
"I think that's the best result I've had as a young manager learning my trade," he said.
"We had five senior players missing so to deliver that performance was terrific. I don't get too high with the highs or too low with the lows but we're a team that is improving in several ways.
"Like all of us on this difficult run, Charlie's been questioned a little but he's answered all of his critics today. It was some goal."