Sean Dyche was frustrated to have a third-successive clean sheet snatched away late on by Everton at Goodison Park.
After 1-0 wins over Newcastle United and Bournemouth - neither of whom registered a shot on target, the Clarets were 10 minutes away from at least a goal-less draw in Carelo Ancelotti's first game in charge of the Toffees.
However, Dwight McNeil gave away possession down the left, and Djibril Sidibe centred for Dominic Calvert-Lewin to head the winner.
After a game of few clear-cut chances, Dyche said: "A strange one, overall I was happy with the gameplan, because we thought, with the new manager, the reaction of the crowd, etc, they might come out on the frontfoot more, and I thought we handled that well.
"The shape was good, without getting as much progress in the game as we wanted, that was part of it, we thought we might have to do that, and I thought we did that well.
"Any efforts they had were from set pieces or distance, and I thought we handled it well.
"Second half I thought we came out and tried to affect it, which is what we thought, that was the plan, and we sort of did, but we couldn't find the margins - neither could they, we couldn't find the details, but a lot of our play was better and still looked defensively organised.
"The two centre halves were terrific,, Popey - not that he had big saves, but his handling, his aggressive nature coming off his line - i thought we were intact.
"Unfortunately we made a mistake trying to play inside football, when we could play for position, not possession, at that stage, just roll it into the corner, get our shape, move up the pitch, and make progress that way.
"But it's a detail within a game of tight margins."
It was McNeil's 38th-straight appearance in the Premier League, 37 of them starts, and Dyche wasn't getting carried away by what will be a learning curve for the youngster: "He's a young lad, I think that's a full season of games from last season to this - fantastic for what was a 19-year-old, just turned 20.
"And he's not made too many mistakes, trust me, it's just a decision moment, and some of that comes with experience.
"We were just a little open on turnover. Credit to them, they played a great cross in, he runs between the centre halves and a good finish.
"But, overall, with a new manager coming in, etc, I thought we handled the game quite well, and probably, possibly deserved a point, and we'd go away saying 'okay, another point on the table.'"
Another clean sheet would have put Burnley out in front in terms of shutouts ahead of Leicester's game against Liverpool, and Dyche mused: "That would have been nice as well, from a team point of view, the defending point of view, was good today, it was just finding the details to open up the opposition, which, over the calendar year, we've done well.
"We've progressed on that side of things by scoring more goals, and looking like we're going to score more goals.
"Within that, a few details, obviously we're still trying to protect Barnesy and get him through games.
"It's one of those things with the two games in three days.
"Good for Robbie to get more minutes, good for Johann, so we are getting people back fit, or really fit, in Robbie's case, really match fit, and getting Johann some minutes."
Ashley Barnes was rested, starting on the bench as he manages a groin injury, as Dyche explained: "It's just an overuse-style injury, it can flare up and then settle down very quickly, we've just got to keep an eye on it, with his training load, which is why we had to make a decision today."
Aaron Lennon also missed out with illness, while Matej Vydra is having compassionate leave after the birth of his child: "Aaron Lennon had been ill over Christmas, and Vyds has had a baby. Not him. That would be amazing. The squad is skinny but we tried to give him a couple of days off just for doing the right thing."
And with the squad stretched, Kevin Long finished as an auxiliary striker: "You're trying to mix it up then, we couldn't really build that momentum, but they probably would have gone slightly deeper - just purely trying to change the feel of it while keeping our two centre forwards on, obviously."
Preparing to face Everton, Dyche wondered whether Ancelotti would revert to type, and he said: "A lot of his history suggests he's had big spells of playing 4-3-3 - with some of the top players in the world, so more or less you could play anything you want with them.
"But early on, and latterly at Napoli, he played a lot of 4-4-2 or a version of it, so we thought they might go a little bit like that, releasing the left back, trying to create a three at the back, but I was pleased because really they played in front of us, it was methodical, but without any real questions asked.
"Then second half they went longer and tried to mix it up, and I thought our centre-halves were excellent, they were certainly doing what they had to do, and, unfortunately, we got unlocked on a mistake of our own, and that's the frustration.
"It's more frustration than anything."
Bar an early chance for Jay Rodriguez, and a couple of openings for Chris Wood - who would have been flagged off-side had he scored, and Robbie Brady, Burnley struggled to create, but Dyche insisted: "We've had ups and downs with that ever since we've been at the club.
"It is the Premier League, it is hard on that side of things.
"If it wasn't, everybody would be scoring loads of goals every week.
"We have to progress as individuals and a team, teams buy it in, but, historically we haven't been able to so we've had to keep developing and I think we have done that well, I really do, so I'm certainly not going to over-question one performance.
"We've found ways to score goals, we've certainly found ways to defend well, and it's a work in progress."