The suppression of heavy quarkonia states in heavy-ion collisions is a phenomenon understood as a consequence of QGP formation in the hot, dense system formed in nucleus-nucleus collisions at the LHC. In addition to hot matter effects in heavy-ion collisions, cold nuclear effects may also affect quarkonia production. Therefore, a full assessment requires detailed studies on the effects present in both A+A and $\textit{p}$+A collisions. Based on $\textit{p}$+Pb data collected in 2013 and $\textit{pp}$ and Pb+Pb data collected in 2015 at the LHC, the ATLAS experiment has studied prompt and non-prompt $J/\psi$ and $\psi\left(2\mathrm{S}\right)$ productions as well as $\Upsilon\left(n\mathrm{S}\right)$ production via the di-muon decay final states. The results of the various measurements are discussed.