Sean Dyche rued missed chances and another penalty that got away in the defeat at Southampton.
The Clarets saw a host of first half chances saved by substitute keeper Kelvin Davis, before George Boyd was denied a spot kick following a dubious challenge from Jose Fonte.
Goals either side of half time, from Shane Long and a Jason Shackell own-goal compounded the Clarets misery.
Boss Dyche said: “I doubt they would have expected to go in a goal up at half time because I felt we played ever so well.
“We came down here, played on the front foot and created four good chances and should have had a penalty.
“That’s three we haven’t been given in recent weeks now and I have no problem with referees, but that was a penalty today.
I ask my players not to simulate, but that might have to change because I must be the greenest manager in the world looking at that.
“Therein lie the margins of the Premier League, unfortunately.”
Davis, who replaced the injured Fraser Forster after only 10 minutes of the game for his first Premier League appearance in 15 months, saved well from Sam Vokes (twice) and Danny Ings in a first half that saw Burnley create the better chances.
Dyche said: “I played with Kelvin many moons ago and he is a fine keeper, but it was more our poor finishing today.
“They were a good height for the keeper and we have to learn that at this level, you have to take those chances.
“I was a bit disappointed with that. I rarely question my strikers because I want them to play with a freedom to miss chances, but today I felt they were very good chances that we should have taken.
“The second half was flat until they got the goal and then it’s tough for us, but we kept trying to effect the game and that’s how we play.
“We never give up, so we’ll dust ourselves down and go again.”