This study examines the residual stress induced by manufacturing and its effect on failure in thermosetting unidirectional composites under quasi-static loading, using Finite Element-based computational models. During the curing process, the composite material develops residual stress fields due to various phenomena. These stress fields are predicted using a constitutive viscoelastic model and subsequently initialized within a damage-driven Phase Field model. Structural tensors are used to modify the stress-based failure criteria to account for inherent transverse isotropy. This influence is incorporated into the crack phase field evolution equation, enabling a modular framework that retains all residual stress information through a heat-transfer analogy. The proposed coupled computational model is validated through a representative numerical case study involving L-shaped composite parts. The findings reveal that cure-induced residual stresses, in conjunction with discontinuities, play a critical role in matrix cracking and significantly affect the structural load-carrying capacity. The proposed coupled numerical approach provides an initial estimation of the influence of manufacturing defects and streamlines the optimization of cure profiles to enhance manufacturing quality. Among the investigated curing strategies, the three-dwell cure cycle emerged as the most effective solution.