If Frank de Boer was already on the brink, then where is he now?

A record-breaking defeat for a manager who last Sunday was uncertain to even make it this far would usually be enough to see him falling from the precipice.

But however painful these 90 minutes at Turf Moor turned out to be, Palace were - according to Sean Dyche - "genuinely the better side" and were improved. It makes Steve Parish's next decision very difficult.

If this was De Boer's final game in charge of Crystal Palace then he can walk away knowing that he should not be apportioned full culpability for the failures of what would become one of the Premier League's briefer and more bizarre managerial reigns.

De Boer is a coach, rather than a manager, and his team carried out what he had tried to drill into them on the training field in their limited time together this week - dominance, possession and increased energy levels. The players showed more verve than at any point this season but let him down at both ends of the pitch, and the club's recruitment over the past 18 months meant that, when he looked to the bench, rather than have a back-up senior striker he was forced to throw on an academy debutant and hope.

Lee Chung-yong's telegraphed backpass gifted Chris Wood the game's only goal and Burnley a 1-0 victory that they sat on for 87 minutes. But the fear for Palace, who haven't scored a goal in their four Premier League games and have been duly punished in each, is that the run goes on far longer. Crystal Palace have lost eight of their last nine games in the top flight extending back into last season. The only one they didn't lose was the one game they scored a goal in. Scoring goals would seem a simple solution to their malaise but no team has ever made that basic act look so difficult.

That run of results also suggests the problem is far deeper. There is genuine quality in the Eagles' first XI but the depth in the squad has been dangerously thinned and it is as if Alan Pardew and Sam Allardyce took out a loan that De Boer is now having to pay back.

The Dutchman saw his side dominate, but get nothing from yet another Premier League match (Getty)

Palace can fairly claim to have been the better side in terms of territory, possession and efforts on goal but the result - and key members of the club's hierarchy have been keen to emphasise that this is "a results business" - was once again missing from the equation. Even an improved performance by many metrics contained some very sterile attacking, predictable and lacking in spark. You wonder what De Boer, knowing the gravity of this match, would have given to have Wilfried Zaha on the field today.

Sean Dyche's teams are well-organised and tough to break down, but when they did give up good chances they always seemed to fall to the most inopportune player. Scott Dann twice had seemingly goalbound strikes halted by desperate last-second interventions. Jeffrey Schlupp blasted over when free in the penalty area. Christian Benteke, the player who this team leans on more than any other with Zaha's injury-enforced absence, had one clear chance but found substitute goalkeeper Nick Pope in sharp form. Then Dann, at the death, had his clearest opportunity yet. He headed wide.

"We missed four or five 100% chances" said De Boer post-match and there was nothing he could do but lament that. His players failed to execute but the energy was back and the chances were at least being created. That is the real quandary for the onlooking Parish after today, this was so vastly improved on what has gone before it but is that improvement enough? Is there enough progress to excuse zero points from twelve?

Crystal Palace's American investors Joshua Harris and David Blitzer are also owners of the Philadelphia 76ers, where they hired a young visionary called Sam Hinkie to run the team. The catchphrase through the hard times was "trust the process" and they did... until they sacked him before he was really given the time to complete his project.

That isn't far off what Harris, Blitzer and particularly Parish need to decide now. Do they trust De Boer's process over results when there were obvious signs of improvement? Or in a season of just 38 games, knowing relegation would be catastrophic and that luck doesn't always even itself out despite the clichés, do they go back to what they know?