Iterative learning control (ILC) is typically applied in practice combined with a feedback controller for time-domain stability. In this closed-loop design with actuator constraints, existing constrained ILC designs suffer from determining the exact input constraint on the ILC controller. This issue brings in an important gap between the existing constrained ILC designs and their real-world applications. This paper gives a systematic consideration of the input constraint problem in the closed-loop ILC design with actuator saturation. A constraint-aware ILC is developed to autonomously determine the constraint on the feedforward controller. The convergence of the constrained ILC process is proved under the framework of alternating projection. Finally, the effectiveness of the developed method is verified on a numerical simulation.