Analysis of the performance of Unmanned Aerial Vehicle (UAV)-enabled communications systems often relies upon idealized antenna characteristic, where the side-lobe gain of UAVs' antenna is ignored. In practice, however, side-lobe cause inevitable interference to the ground users. We investigate the impact of UAVs' antenna side-lobe on the performance of UAV-enabled communication. Our analysis shows that even for a very small antenna's side-lobe gain, the ground receiver can experience substantial interference. We further show that a rather large exclusion zone is required to ensure a sufficient level of protection for the ground receiver. Nevertheless, in a multiple-antenna setting for the ground users, even when such a large exclusion zone was in place, UAVs' antenna side-lobe creates a high level of correlation among the interference signals received across receive antennas. Such a correlation limits the system ability to exploit channel diversity in a multiple-antenna setting for improving capacity. We then quantify the impact of UAVs' antenna side-lobes on the overall system performance by deriving the corresponding loss of the achieved capacity in various communications environments. We provide a new quantitative insight on the cost of adopting non-ideal UAV antenna on the overall capacity. Our analysis also shows that the capacity loss can be confined by careful selection of system parameters.