Clusters of galaxies probe the large-scale distribution of matter and are a useful tool to test the cosmological models by constraining cosmic structure growth and the expansion of the Universe. It is the scaling relations between mass observables and the true mass of a cluster through which we obtain the cosmological constraints by comparing to theoretical cluster mass functions. These scaling relations are, however, heavily influenced by cluster morphology. The presence of the slight tension in recent cosmological constraints on $\Omega m$ and $\sigma 8$ based on the CMB and clusters has boosted the interests in looking for possible sources for the discrepancy. Therefore we study here the effect of active galactic nucleus (AGN) feedback as one of the major mechanisms modifying the cluster morphology influencing scaling relations. It is known that AGN feedback injects energies up to 10$\mathrm{<mrow\; data-mjx-texclass="ORD">62</mrow>}$ erg into the intracluster medium, controls the heating and cooling of a cluster, and re-distributes cold gas from the centre to outer radii. We have also learned that cluster simulations with AGN feedback can reproduce observed cluster properties, for example, the X-ray luminosity, temperature, and cooling rate at the centre better than without the AGN feedback. In this paper using cosmological hydrodynamical simulations we investigate how the AGN feedback changes the X-ray morphology of the simulated systems, and compare this to the observed Representative $XMM-Newton$ Cluster Structure Survey (REXCESS) clusters. We apply two substructure measures, centre shifts ($\omega$) and power ratios (e.g. $P3$/$P0$), to characterise the cluster morphology, and find that our simulated clusters are more substructured than the observed clusters based on the values of $\omega$ and $P3$/$P0$. We also show that the degree of this discrepancy is affected by the inclusion of AGN feedback. While the clusters simulated with the AGN feedback are in much better agreement with the REXCESS $LX-T$ relation, they are also more substructured, which increases the tension with observations. When classified as non-relaxed or relaxed according to their $\omega$ and $P3$/$P0$ values, we find that there are no relaxed clusters in the simulations with the AGN feedback. This suggests that not only global cluster properties, like $LX$ and T, and radial profiles should be used to compare and to calibrate simulations with observations, but also substructure measures like centre shifts and power ratios. Finally, we discuss what changes in the simulations might ease the tension with observational constraints on these quantities.