It has happened to me in the past. I came back several times before it actually worked. Just a glitch but it did eventually work. Carrying the other claws did not make any difference though. I got mine to work on like the third or fourth try.
After you select the correct animal alignment on the nearby pedestals, you are inserting the claw into the key hole on the door itself, right? Also, sometimes after you've set animal #1 and then go set #2 and #3, you might find that #1 has moved and must
be set again. After you've set all 3, you should do a visual double-check to make sure they haven't changed.