Defender Martin Kelly scored the only goal of the game in the first minute of stoppage time at the end of the first half as we exited the competition at the fifth round stage.
Dele Alli had earlier gone close on a couple of occasions, seeing his diving header blocked on the line before hitting both posts with one effort, but it wasn't to be our day.
Spurs (4-2-3-1): Vorm, Walker, Wimmer, Dier, Rose, Dembele (Eriksen 46), Bentaleb, Alli (Mason 80), Onomah, Son (Chadli 67), Kane (c). Substitutes (not used): McGee, Alderweireld, Trippier, Winks.
Palace (4-4-2): Hennessey, Ward, Dann, Delaney (c), Kelly, Zaha, Cabaye (Jedinak 80), Ledley, Mutch, Wickham, Adebayor (Bolasie 76). Substitutes (not used): McCarthy, Mariappa, Campbell, Lee, Gayle.
Goals: Palace – Kelly 45+1.
Yellow cards: Spurs – Rose; Palace – Cabaye, Bolasie.
Referee: Craig Pawson.