depends how it broke off?
YOu sure its just a tentacle and not a small split? If its just a tentacle, I wouldnt worry
double check your water params, rejecting tenticles isnt good. how long have you had it for? what/if anything do you feed it and how often, whats the flow like, has it recently moved and any details about it you can include.
that may be the problem, try feeding it something small sized and a small amount. i never suggest any foods of large size as i feel nems use more energy digesting them then the energy they gain. also what lighting is it under?