The impact of the addition of 0.5 wt% multiwall carbon nanotubes (MWCNT) on the quasi-static transverse compressive resistance and damage evolution of unidirectional glass fiber reinforced composite (FRC) fabricated by resin transfer molding is investigated. The degradation of macroscopic mechanical properties such as elastic modulus and compressive strength vs. plastic strains are correlated with crack density and microcrack propagation behavior including analysis of failure phenomena such as interface debonding, matrix cracking and interface cracking. The experimental campaign includes compression tests with monotonic and cyclic loads on cubic specimens in the out-of-plane (0°) and transverse (90°) directions for masterbatch MWCNT-based and CNT-free glass FRC. In the monotonic case, the elastic modulus and maximum compressive strength increased for the glass FRC with 0.5 wt% CNTs, particularly in the transverse (0°) direction by 11% and 13%, respectively. Under cyclic loading, the elastic modulus degradation stagnates at a lower plastic deformation for composite with 0.5 wt% CNTs. In addition, CNTs reduces by 20% the cumulative plastic deformation in the 0° direction and almost 30% in the 90° direction. At the microscopic scale, image analysis showed that the CNTs improved the properties of the interface by delaying decohesion failure and reducing by around 30% and 40% the computed crack density in the 0° and 90° loading direction, respectively. In addition, image analysis in the out-of-plane direction (0°) shows that fiber-matrix decohesion is predominant before crack propagation at the interlaminar level and prior to final failure. By contrast, at 90° loadings, no decohesion is observed and crack propagation is almost purely interlaminar. Finally, the addition of 0.5% MWCNTs to the glass FRC increases the mechanical resistance of the composite material in the transverse direction demonstrated by the delaying of cracks during the failure analysis of different cycles as well as the decrease of the elastic modulus degradation and increase of compressive strength.