With ten home wins providing the backbone to their season past year, Burnley ironically lost their first game at Turf Moor this season.
Asked whether the battling display, which should have earned the London club at least a point, had bought him some time, De Boer said: "I don't know, they have to decide".
Palace must have feared this, again, would not be their day - a feeling reinforced when Tarkowski summed up his superb performance with another goalline clearance from Dann, who then headed wide of a near open goal in the dying minutes as the Clarets clung on to a precious three points.
Palace have typically gone for managers who are known for a no frills, defensive, long-ball style of play that can hit teams on the break if need be and that is the kind of players that they have at their disposal.
While the pair are not particularly noted for their man-on-man defending against skillful players, they showed they were more than a match for nearly everything Spurs threw at them. The Frenchman is not match fit following his lack of action at Anfield but De Boer says Sakho "is already a very good influence in the dressing room and in training". Still, time is a luxury few bosses have - and judging from the look on chairman Steve Parish's face in the stands, the powers-that-be are not happy with what's happening on the pitch.
"I can not believe we lost", said De Boer.
"I think this is a good starting point and this is what I want to see from any team that I manage".
"But that's football, sometimes you don't get what you deserve".
Meanwhile, the Eagles have endured a poor start under new manager Frank De Boer.
Schlupp should have levelled the scores with just under 20 minutes remaining, finding himself with space inside the penalty area, but he got everything wrong, leaning back and firing wildly over the crossbar. I feel like I can keep progressing and do even better.
"You can not expect to win every game, it's a work in progress still".
"It has always been my goal to play in the Premier League and when Burnley came in, I found out after the first bid was rejected how keen they were and things moved very quickly after that". "We all want to rush through this game and every player, every media outlet, they all want players to be exceptional within three games of playing professional football".