Jeff Hendrick and Sean Dyche both felt the Clarets were denied a “blatant” penalty that could have proved decisive in the Huddesfield stalemate.
The Irish midfielder crumpled under a challenge from Jonas Lossl jus after the hour mark of a game that Burnley dominated for long periods.
Referee Paul Tierney felt there was no contact from the Danish goalkeeper.
Hendrick said: “I tried to go around him and felt contact that made me go down, but the ref said he didn’t think it was a dive and he thought I lost my footing.
“I thought we fought hard today, so it’s disappointing and unfortunate that we didn’t get the penalty, but the one thing we always say is that if we can’t win a game, then we don’t lose it.”
Dyche added: “I don’t need to say to much about it and I hope the television show it and show it again because it’s impossible that it’s not given as a penalty, in my opinion.
“I believe the referee said he thought Jeff lost his footing. I would argue there is a clear reason why he did so and I think we can all agree that!
“I am worried for the game at the minute because I am in a league where others are given for all sorts of reasons, but that’s as blatant a penalty as you will see.
“What is peculiar about football at the minute is that when players go down in a diving manner and throw their arms about they get those.
“Jeff has gone down in natural manner after his back foot is clearly taken away from him and doesn’t get it. It seems that people who go down in a theatrical way do get them.”
The Clarets carved out a number of good chances, notably in the first half when Steven Defour, Kevin Long and Ashley Barnes all cameclose to breaking the deadlock.
Scott Arfield and former Town striker Nahki Wells also saw second half shots saved by Lossl as Burnley picked up their third successive draw on the road to end the calendar year in seventh spot in the Premier League on 34 points.
Dyche added: “Other than that penalty decision, I am really pleased, performance-wise. Physically we were really strong.
“We created a number of chances and kept on the front foot. The lads have given a really good account of themselves and we restricted them to very little with our keeper not having a lot to do.
“That’s three away games out of four and three really good points on the board. We deserved more today, but you don’t always get what you deserve.”