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Lattice size dependency of critical temperature of Ising nanofilms and nanotubes on the square lattice have been investigated Using Cellular Automata simulation approach. The obtained values of critical temperature for single-layer nanofilm on the infinite size of lattice is equal to 2.36, the corresponding value for single-layer nanofilm on the honeycomb lattice was 1.45. The effects of length and diameter of nanotube on the critical temperature were also studied. For equal size lattices, the critical temperature values of nanotube are larger than those for nanofilm. The critical temperature of a single-layer nanotube on the infinite size lattice was calculated as 2.37. The proximity of the values for the critical temperature of nanofilm and nanotube in the infinite size of lattice reflects the fact that by increasing the length and diameter of the nanotube, its magnetic behavior tends to be as nanofilm. Such studies seems to be of particular importance in providing tabulated data on the effect of lattice size on critical temperature and magnetic behavior of magnetic nanomaterials.