The Eagles were the better side for large parts of the encounter at Selhurst Park as their compact system restricted Spurs to only a handful of opportunities.
But Christian Eriksen broke the deadlock late on to keep Spurs' title hopes alive and leave Palace two points short of the 40-point mark.
Allardyce's side were in action against Liverpool as recently as Sunday and the 62-year-old is adamant such a quick turnaround made it difficult for his players to repeat their Anfield heroics.
"Outstanding team effort by the players, who have had less time to recover against an exceptionally good side," Allardyce told Sky Sports.
"Our application was outstanding and we gave Tottenham a hell of a game in the first half.
"But of course it would happen that we would tire given the lack of recovery time compared to Tottenham.
"A terrific goal by [Christian] Eriksen but a shame for the lads they could not hold out," Allardyce added.
Palace remain seven points clear of the drop zone with just five games left to play and have all-but retained their top-flight status for another season.
But the south Londoners may have seen the last of Liverpool loanee Mamdoua Sakho.
The Frenchman was stretchered off with suspected knee ligament damage after a clash with Harry Kane and is set to undergo a scan to assess the damage he has suffered.
Meanwhile, Palace's gruelling schedule it set to continue this weekend with the Eagles set to travel to Burnley on Saturday evening.