Due to the design defect, adjustment error, thermal deformation and gravity deformation in orbit, the bad optical antenna of the communication receiving terminal in an inter-satellite laser communication link will induce aberrations to the received wave-front. This will cause attenuation of the received power and deterioration of the bit error rate (BER) performance. The calculation model of the compensated and normalized received power is established when the received light spot is pointed at the center of the focal plane and the limited receiving radius is considered. The numerical results show that, for receivers with a single first-order Zernike mode wave-front aberration, the primary spherical aberration has the most influence on the received power attenuation, and for receivers with the same type aberrations, higher-order Zernike aberrations have more influence on that. The universality of the result for different antennas is verified by introducing a characteristic radius and a relative receiving radius. Some suggestions are proposed to lower the requirements of the wave aberrations control, thus reducing the difficulty of optical design, structural design, thermal design, assembly and adjustment. The outcome of this study would contribute to the design of the inter-satellite laser communication systems.