Sean Dyche insisted he was more frustrated than disappointed after the Clarets came close to spoiling Carlo Ancelotti’s big day.
Dominic Calvert-Lewin’s late header made it a winning start for the Italian as Burnley threatened to make it three clean sheets on the bounce in a game of few chances.
And Dyche was left to rue a defensive lapse as the game appeared to be petering out in to a dour stalemate.
“We are more frustrated than disappointed, because the game was heading towards a 0-0 and we’d have taken that today, with all that was going on at Everton,” said the Clarets boss.
“I don’t normally like to take a 0-0, but I would have, but unfortunately it’s gone away from us following a mistake.
“It was a game plan by design. We thought there might be a reaction to the new manager and that we’d have to absorb the game, especially in the first half and I thought we did that quite well.
“There wasn’t a lot in it and I’m pleased in that sense. They’ve spent a lot of money and after a top-class manager walks in the building, you would expect a reaction.
“They ended up playing in front of us methodically and quite slow, and that was a part of the plan.
“At half time we thought we could progress more, which we did, and I thought we took the game on in the second half.
“They went a lot longer and I thought our two centre halves were excellent. For them to be on the wrong end of a potential clean sheet was harsh today.”
The crucial moment arrived in the 80th minute, when Dwight McNeil lost possession on the touchline and Djibril Sidibe crossed from the right for Calvert-Lewin to find the bottom corner with a diving header.
“Dwight has done brilliantly for us and that was a part of his learning curve,” added Dyche.
“He’s tried to play inside football when we are open, but it was cut out and they capitalised quickly with a good ball in.
“We were just a bit dis-organised and stretched as we were in possession at that moment, and that’s where you learn to play for position, not possession, by shaping it down the line and gathering your shape.
“But they are the moments and that’s how players learn. He is a fantastic young player and he will learn from that.”
Dyche, who opted for Bournemouth goal hero Jay Rodriguez to partner Chris Wood as the club continue to nurse Ashley Barnes’ troublesome groin injury, added: “We knocked on the door a few times, without finding that golden moment, and we’ve managed to find that well in the last calendar year.
“But we never found those killer moments today. That is something we have to work on constantly and, unfortunately, they found it today.”