A quantum-mechanical analysis of feedback cooling [see Phys. Rev. Lett. 94, 153002 (2005)] of atoms trapped in a far-off-resonant optical lattice is presented. The model considered is valid for ultralow energies of atoms, thus, allowing for the study of an ultimate cooling limit. The influence of the measurement-induced noise and feedback-induced atom-atom correlations on the cooling efficiency is discussed. It is shown that there are regimes where the quantum noise can be effectively compensated for.