The Clarets missed out on a first quarter-final place in the FA Cup for 18 years as Championship side Bournemouth ended an even longer wait.
The Cherries hadn’t advanced into the last eight since 1957 but a goal from Sam Surridge mid-way through the first half and a late penalty from ex-Claret Junior Stanislas was enough to make them the first name in the hat.
And the Clarets, stretched by injuries and with half an eye on their up-coming Premier League fixtures, could have no complaints as they bowed out in a passive style.
A brief rally after half-time raised hopes of a successful comeback to prolong their interest in the competition and put a possible Wembley semi-final only one more win away.
But a missed Jay Rodriguez chance was the nearest Burnley came to levelling and despite an attempted injection of fresh legs from the bench, Bournemouth weren’t overly stretched in their smooth passage through into almost uncharted waters.
The Clarets made eight changes to their starting line-up, including a late switch which saw Anthony Glennon replace Erik Pieters to make his full senior debut.
Bournemouth swapped one player fewer from the side that secured a win in Jonathan Woodgate’s first game in charge last weekend after the former England defender stepped up to replaced former Burnley assistant manager Jason Tindall.
But the Cherries still had as much experience in their ranks as a Burnley side also missing five senior men through injury.
And the visitors were the better side in the first half as they carried a constant threat on the break.
Philip Billing put an early chance into the side netting from Surridge’s pull-back but when Bournemouth attacked down the other flank, they went ahead with 21 minutes gone.
Jack Stacey’s over-lapping run saw him get behind the Clarets’ defence and when he squared the ball, former England Under-21 international Surridge was left with a simple tap-in.
The Clarets must have been glad not to go further behind before half-time and Bailey Peacock-Farrell had to be alert to prevent Dale Stephens – who had fired over the top from Burnley’s only real chance – from heading into his own goal from a Bournemouth corner.
Bournemouth keeper Asmir Begovic was finally called into action four minutes after the re-start as he kept out an angled effort from Matej Vydra after a flick-on from Rodriguez had given his strike partner a rare opening.
And the Clarets then went close to an equaliser twice in a matter of minutes as they began to build some momentum.
Begovic just managed to divert a fierce Dwight McNeil drive around his left-hand post and Rodriguez then missed a glorious chance to add to his FA Cup tally.
The striker had scored 10 goals in his last 12 starts in the competition – including a double in a fourth-round win at Fulham – but after a storming run from Jimmy Dunne and a Vydra mis-cue had left him perfectly placed in front of goal he could not keep down his attempted finish and lifted the ball over the bar from a couple of yards out.
Captain Phil Bardsley then sent a skidding effort just wide as the Clarets kept pushing to keep their hopes alive and with 25 minutes to go, Dyche sent on Ashley Westwood in a bid to retain the initiative.
Ten minutes later boss Sean Dyche made his final play when he made a triple substitution, including changing both front men in the hope of carving out another big chance to potentially take the tie into extra-time.
But Bournemouth looked to have ridden out the spell of pressure and two minutes from time they made sure of their passage through when Stanislas converted from the spot after Kevin Long had fouled Surridge to cap a disappointing night.
Burnley: Peacock-Farrell; Bardsley, Long, Dunne, Glennon; Gudmundsson (Lowton 75), Stephens, Benson (Westwood 66), McNeil; Rodriguez (Barnes 75), Vydra (Mumbongo 75). Substitutes: Norris, Tarkowski, Mee, Nartey.
Booked: McNeil, Bardsley
Bournemouth: Begovic; Stacey (Mepham HT), Carter-Vickers, S Cook, Rico; Pearson, Lerma; Brooks (L Cook 65), Billing, Stanislas; Surridge. Substitutes: Dennis, Kelly, Zemura, Kilkenny, Anthony, Danjuma, Saydee.
Booked: Lerma.
Referee: Darren England