Disappointed Clarets boss Sean Dyche felt his side didn't find the moments of quality required to open up 10-man Leicester City, as they were condemned to a fourth defeat on the spin.
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Burnley had a chance to gain ground on Cardiff City, who occupy the final relegation slot, but remain two points clear of the Bluebirds, who now have a game in hand at home to Chelsea.
Leicester had Harry Maguire dismissed inside four minutes, before taking the lead through a James Maddison free kick.
Dwight McNeil equalised with Burnley's 100th Premier League goal at Turf Moor, but Wes Morgan headed a last-minute winner for the Foxes.
Dyche said: "I'm mostly frustrated, but disappointed. You can't help be disappointed, to concede a goal that costs you in the dying embers of the game is obviously disappointing, particularly as it was completely avoidable.
"We didn't need to give the corner away in the first place.
"First half we didn't quite get to grips with it, that's obvious, without making too many chances they still opened up pockets of play against us.
"We just didn't find the moments, apart from a really good goal from Dwight - and he was another shining light again.
"But overall, first half we didn't really effect the game, a couple of maybes, but we didn't really control the game.
"Second half we had a chat and controlled the game, and by the end, you're kind of waiting for the moment of quality, and clarity, and we didn't find it.
"A couple of maybes again, Dwight's unlucky from distance and one lands for Corky, which is a really good chance, Vyds gets in behind...
"But the real ,moments, the clear moments, we didn't quite find them, as much as we dominated the ball.
"The crosses we know are the real hard ones to deal with, we didn't find those.
"And then in the last stage of the game, you're always fearful about a set piece because of the 'what ifs?'
"And unfortunately they scored,"
Kasper Schmeichel wasn't worked enough, despite Burnley bossing the ball, and Dyche admitted: "He makes a save from Vyds, but we should be, not testing him, scoring on a couple of occasions, but we didn't.
"It can be difficult, 4-4-1-1 away from home, they're making defensive substitutions at the end, so they're thinking 'we'll take this'.
"You have to keep knocking on the door and opening up the moments, and we nearly did, but that's been a challenge ongoing for years here, and certainly this season, when we've had good amounts of play, good possession - same against Palace.
"You have to win games and we never found the moments that count, the real quality you need, to score.
"Credit to Leicester, they camped in, looked for the counter - which they didn't too too many times - and go away with the win.
"We've had to do that many times."
Dyche was frustrated to see Charlie Taylor denied what looked a blatant penalty after having his legs clipped by Wilfred Ndidi, but accepted: "I just think it's a sad state of the game where people can touch you on the shoulder and somehow your legs buckle, and it's a penalty, and Charlie Taylor falls naturally...I've seen it on the monitor and I think you do well to find he hadn't touched him.
"If you touch them on the arm, your legs go from under you, but you get touched on the foot and your leg's not allowed to go from under you.
"But he falls naturally...I feel for the referees, I think their eyes are trained to diving and all that nonsense, that when someone does a real fall, they don't get a penalty.
"But that's no excuse, we should have take care of ourselves.
"At 1-1, that's a really big moment though."