Charlie Austin's strike in the first half was enough to secure the three points for the Clarets at The Valley.
Dyche told the club's official website: "That's the best win of my managerial career. We lost five men and I asked them to man up. They did that fantastically well.
"It was a goal worthy of winning any game. It was a constant barrage in the second half and we dealt with everything."
Following their win Burnley are 11th in the Championship, eight points adrift of the playoff places.