The $J/\psi$ $p_T$ spectrum and nuclear modification factor ($R_{\textit{AA}}$) are reported for $p_T < 5$ GeV/c and $|y|<1$ from 0-60% central Au+Au and Cu+Cu collisions at $\sqrt{s_{_{NN}}} =200$ GeV at STAR. A significant suppression of $p_T$-integrated $J/\psi$ production is observed in central Au+Au events, with less suppression observed in Cu+Cu. The $p_T$ dependence of the $R_{\textit{AA}}$ is observed to increase at a higher $p_T$ region. The data are compared with the previously published RHIC results. Comparing with model calculations, it is found that the invariant yields at low $p_T$ are significantly above hydrodynamic flow predictions but are consistent with models that include color screening and regeneration.