Lewis McGugan made no mistake from 12 yards for the visitors after Kevin Long collided with Henri Lansbury at the end of a turgid game, but Dyche felt Miller should have blown the full-time whistle well before that point.
Junior Stanislas' second-half goal had looked to be enough for the Clarets in a contest between two decidedly weary teams after their exploits earlier this weekend.
"I feel sorry for our fans, because yet again they've witnessed an incredible situation where we can't just win against an opposition, we've got to beat everything else," Dyche fumed.
"I'm disappointed in the whole referee's performance and I'm sick of talking about it because I shouldn't have to. But it's not the first time as we know; it's been a constant issue since I've been at this football club. I don't know what it is, but that isn't good enough.
"I had a word with him [Miller] and he said he was more interested in the fact we were late for kick-off. I was really amazed he when he told me that."
- Sports & Recreation
- Henri Lansbury