They now find themselves second from the bottom, and according to recent reports, De Boer could face the sack if Palace don't win on Sunday.
They have been architects of their own downfall, their problems caused in part by misguided attempts to pass the ball.
Palace were missing Wilfried Zaha, Ruben Loftus-Cheek and Mamadou Sakho for this trip to the northwest; had the trio been available, things may have been panned out differently for De Boer's side.
The Dutchman's future has been questioned by some fans and media after just three games of the season with Palace yet to pick up a point. On each occasion, Palace have had vast amounts of possession and done little constructive with it. While Palace wrestle with an identity crisis, Burnley know who they are and what they have to do. "A very sloppy goal", De Boer admitted.
The former Leeds striker punished a woeful backpass by Palace's South Korean winger Lee Chung-Yong.
The Eagles had a shocking start to the game, when on three minutes Lee made a awful back pass which was lapped up by Burnley striker Chris Wood, and his shot from distance was easily slotted past Wayne Hennessey. His first start brought an early decider. It may prove an accurate prediction, though the manager sounded unworried.
"I'm focusing on what I can control - I couldn't do much more than this", he said.
They pushed and pushed for an equaliser, and Pope made a fine save from Benteke after he had broken into the penalty area for what was Palace's best chance of the match.
Wells says he is healing well from the surgery and looking forward to his new work surroundings. "(The future) is for other people to decide but while I'm the manager of Crystal Palace I will give 100%", he told reporters.
"I'm very disappointed with the result. I'm convinced we are going to achieve it".
This has led to reports suggesting De Boer could be replaced if he cannot turn results around, but he remains confident after talks with Parish. "If I leave, I want to go through the front door. I will sign for this every game if we create that amount of chances". The team have also given up six goals while scoring zero. Burnley manager Sean Dyche said he had some empathy with De Boer and conceded they had deserved more. For Palace, Christian Benteke is available at 21/10 odds. Yet the damning element for Palace was that they rarely troubled a Premier League debutant.
Not long after that, Burnley goalkeeper Tom Heaton collided with a team mate and injured his shoulder.
Crystal Palace's Andros Townsend reacts after the final whistle of his side's defeat. "It was quite dynamic". He attributed that to De Boer's decision to jettison his favoured 3-4-3 formation for a more familiar 4-3-3. Changing system, however, was simpler than changing their fortunes.
"When you see players do well on loan, it means they are flexible to the challenges", said Dyche.