In an end-to-end encounter, with plenty of chances created, the Clarets fell to a narrow 3-2 defeat at home to Fulham on Saturday evening.
It was a lively first-half, as Emile Smith Rowe put Fulham ahead inside six minutes, coasting in unmarked from a corner to prod the ball home from close range.
Burnley were then on terms midway through the half when Lesley Ugochukwu slotted home with aplomb from a perfectly weighted Josh Cullen through ball.
But the lead lasted just ten minutes, as Harry Wilson played provider for the Cottagers' second, sending a fine ball to the back post, which Calvin Bassey - gifted the freedom of the six-yard box - nodded home to restore the visitors' lead.
The Clarets had a number of good chances to equalise at the start of the second half, but - having squandered their opportunities - they were caught with the sucker punch just before the hour, when Wilson curled home a fine finish from a swift Fulham counter-attack to make it 3-1.
Substitute Oliver Sonne pulled one back with five minutes of normal time remaining, slotting home in style on the volley after a great first touch, but that was as good as it got for Parker's side, who succumbed to a 3-2 defeat.
Head Coach Scott Parker made two changes from the side that played Newcastle United last weekend, with Quilindschy Hartman and Axel Tuanzebe coming in for the suspended Kyle Walker and Lucas Pires.
After a lively start from the Clarets, it was the Cottagers who broke the deadlock with nine minutes on the clock.
A corner into the area was met by the oncoming run of Smith-Rowe, who steered it in with a first-time finish to give the visitors the lead.
The Clarets responded well to going a goal behind, however, creating a chance of their own just a minute later, but Ugochukwu’s effort from Jacob Bruun Larsen’s well-timed through ball was kept out by Bernd Leno.
Burnley weren't made to wait too long for their equaliser, though, levelling terms midway through the half.
Some great build-up play saw Hartman, Bruun Larsen and Cullen all linking up, before the skipper threaded a lovely ball into the path of Ugochukwu to slide home with a cool and composed finish.
Despite the hosts clawing the scores level, Fulham regained their lead on the half-hour mark, as Bassey headed in from close range following Wilson’s cross into the box, after the Cottagers recycled the ball from a corner kick.
However, in a lively opening 45 minutes, the Clarets came close to equalising for a second time, as Armando Broja saw his effort saved following a quick free-kick, before the lively Wilson then went up the other end and saw his deflected strike, owing largely to a fine last-ditch Hartman tackle, saved by Dubravka.
The final opportunity of an end-to-end first-half fell to Ugochukwu, with the midfielder seeing his low volley from the edge of the box pushed wide by Leno.
Burnley came out on the front foot and carved open a glorious chance early in the second half, when Bruun Larsen intercepted a Fulham pass-back towards Leno, but the Dane forward could only fire straight at the Cottagers’ goalkeeper.
However, it was Fulham who struck again just moments after that opportunity, when a swift counter-attack saw Wilson guide a shot home into the bottom left hand corner.
As the game reached the hour mark, Parker made a double change with Zian Flemming and Marcus Edwards coming on for Foster and Florentino.
But it was Fulham who continued to create the better chances of note, as Antonee Robinson unleashed an effort from inside the area, but the full-back’s effort sailed over the crossbar.
Flemming went close with six minutes of normal time to play, stinging the palms of Leno, but from the next chance of note, the hosts pulled one back.
Sonne's first touch at the back post was exquisite and his second wasn't bad either, as he slotted home a cultured 10-yard volley to give the Clarets hope.
That's all it proved to be, however, despite six minutes of added time, as Fulham held on for the three points.
Burnley: Dúbravka, Hartman, Estève, Tuanzebe (Sonne 77), Bruun Larsen (Anthony 77), Ugochukwu (Trésor 83), Foster (Flemming 62), Florentino (Edwards 62), Ekdal, Cullen, Broja
Unused substitutes: Weiss, Worrall, Tcahouna, Laurent
Fulham: Leno, Tete, Bassey, Andersen, Jimènez (King 79), Wilson (Adama 89), Berge, Iwobi (Lukic 79), Chukwueze, Smith Rowe (Castagne 89), Robinson
Unused substitutes: Lecomte, Reed, Cairney, Cuenca, Kevin
Goals: Smith Rowe 9' Ugochukwu 21', Bassey 30', Wilson 58', Sonne 86'
Attendance: 19,739