So where does Tuesday’s result leave Palace?
In stark contrast to his opposite number, Oliver Glasner looked ashen-faced when he addressed the media after the full-time whistle, which was greeted by loud boos from the Palace supporters.
Having watched his team arrest a 12-match winless run against arch rivals Brighton last time out, Glasner looked set to mark his 100th match in charge of the club with another morale-boosting win after Strand Larsen’s double.
But Palace froze after Mejbri had pulled a goal back for Burnley, who took full advantage of the hosts’ inertia to inflict one of the most painful defeats of the Austrian’s Selhurst Park tenure.
“It’s not acceptable,” Glasner, who is leaving the club in the summer, told TNT Sports. “I can’t explain it. Maybe [the first 39 minutes] were too easy.
“The start was very good. We controlled everything, [but] I’ve watched all the goals back and it’s just not acceptable how we defended as a team – just jogging around, not in the duels, not in the second balls.”
Another issue, according to Glasner, is the presence of a Marc Guehi-sized hole in the Palace defence.
The England defender left for Manchester City for an initial £20m last month in a move which incurred the wrath of Glasner, who announced his own departure not long afterwards.
“Right now, we don’t have someone on the pitch who leads the team in these moments, who makes players calm and decides the meaning of the game,” he said.
“I praise the boys very often for their effort. When you throw the game away like we did, you don’t deserve to win.”
Palace are still eight points above the bottom three – a sizeable cushion, but one not comfortable enough for a side with only one win in all competitions since 11 December.
Defeat at home to Wolves in their next league game really would set alarm bells ringing.