Dyche brought the pair from Elland Road to Turf Moor this summer and the third-round draw gave them an early reunion with their old side, as well as a vociferous group of supporters who barracked them from the first whistle.
Wood scored twice from the penalty spot after coming off the bench, once in normal time to help force a 2-2 draw and again in a shootout which the Clarets lost 5-3.
"It's a strange business, football," mused Dyche.
"Twenty-odd million they've made for a club (in transfer fees) and they get slaughtered. I don't know any more how fans react to players, ex-players, all that stuff, but that's football now.
"Those two have been fantastic servants to Leeds, if I'm honest. But Woody has done fantastically, walking onto our pitch and scoring, and again in the shootout."