A study of $J/\psi p$ resonances in the $\Lambda_b \rightarrow J/\psi p K$ decays with large $m(p K^-)$ invariant masses by the ATLAS experiment at the LHC is presented. The analysis is based on a combined sample of $pp$ collision data at centre-of-mass energies $\sqrt{s}=7\,$TeV and $8\,$TeV corresponding to integrated luminosities of $4.9\,$fb$^{-1}$ and $20.6\,$fb$^{-1}$, respectively. Although the data prefer the model with two or more pentaquark states, the model without pentaquarks is not excluded. The pentaquark masses and widths obtained using the model with two pentaquarks are consistent with those from the LHCb experiment.