Typical computer-based parameter optimization and uncertainty quantification of the additive manufacturing process usually requires significant computational cost for performing high-fidelity heat transfer finite element (FE) models with different process settings. This work develops a simple surrogate model using a feedforward neural network (FFNN) for a fast and accurate prediction of the temperature evolutions and the melting pool sizes in a metal bulk sample (3D horizontal layers) manufactured by the DED process. Our surrogate model is trained using high-fidelity data obtained from the FE model, which was validated by experiments. The temperature evolutions and the melting pool sizes predicted by the FFNN model exhibit accuracy of and , respectively, compared with the FE model for unseen process settings in the studied range. Moreover, to evaluate the importance of the input features and explain the achieved accuracy of the FFNN model, a sensitivity analysis (SA) is carried out using the SHapley Additive exPlanation (SHAP) method. The SA shows that the most critical enriched features impacting the predictive capability of the FFNN model are the vertical distance from the laser head position to the material point and the laser head position.