Materials design considering reliability and sustainability has been a challenging issue. Machine Learning (ML) model of the structure-property relation based on large data from reliable physical models becomes a new and promising approach to confront this challenge.  The present work demonstrates such type of study to examine the microstructure features of fiber networks in paper materials and to reveal the impact of their morphological sensitivity on mechanical properties. After the generation of a ``big'' dataset of realistic fiber network samples, morphological feature data, including interfiber contact properties were extracted and statistically evaluated. By performing cohesive finite element simulations, the mechanical properties including failure strain, effective stiffness, and maximal stress of fiber networks under tensile test are determined and served along with structural feature data for the ML analysis. ML models were trained and tested using different ML algorithms, of which the Gradient Boosting method achieved a performance score of approx. 0.9 for all mechanical properties of such complex fibrous structure.It was found that ''disorderness'' represented by the standard deviation of fiber network orientation and the mean contact area size as derived properties to be the most influential factors to the failure strain and effective stiffness. Whereas the failure strength was driven by the homogeneous distribution of the contact areas. The results validated the strong orientation dependence of fibrous materials in experimental observations and enlighten the importance of sensitivity as feature parameters and the striking potential of ML for material optimization.