Matt Taylor and Jack Collison both netted from the spot in the closing 15 minutes on Tuesday night as Burnley's eight-match unbeaten run came to a crashing halt.
The Championship leaders had the better of their Premier League opposition in the first half and could have broken the deadlock when Kieran Trippier's thunderous free-kick rattled the woodwork in the second period.
However, momentum switched when referee Robert Madley pointed the spot after Jason Shackell brought down Kevin Nolan inside the area but Dyche was unhappy with the official's call.
"I asked the referee and he said he was happy with his view; I wasn't as happy with his view," the Clarets boss said.
"I think it's a very difficult position to see a penalty from. He's behind the play and three or four players, but I always respect referees' decisions and that's the way it is.
"There was no major contact, certainly not enough to bring them to the floor, but the referee has to make a decision and he's made one."
Dyche celebrates his one-year anniversary at Burnley on Wednesday, yet his celebrations were soured further when Treacy, chasing back to try and stop Collison firing home, tripped the Welsh midfielder in stoppage time to earn a slightly early bath.
"The hard one to take is the fact that, in the modern game, does that really warrant a sending off?" asked Dyche.
"The rule states it does but it is bizarre really. I think the penalty is enough, to be honest.
"They're the rules, I'm not stating we should change them, I'm just saying it was a nothing incident, it wasn't malicious, he was trying to get back and stop a goal."