Transportation networks are crucial for social and economic activities but are susceptible to disruptions. Rapid quantification of the impacts of network disruptions can assist in planning recovery efforts. However, gathering timely and comprehensive information for assessing transportation network state is often challenging and not always possible. This study introduces a network assessment strategy to estimate total link capacity reduction and origin–destination (OD) demand matrix (CRDM) for disrupted transportation networks subject to limited information, i.e., link travel time accessible from smartphone-based trajectory data. The CRDM problem can be formulated as a bi-level model, optimizing estimates of externally caused capacity reduction and OD demand matrix in the upper level while solving the user-equilibrium-based traffic assignment in the lower level. The proposed bi-level model with a generalized least squares (GLS) objective (to minimize the discrepancy between observed and estimated travel times) does not yield a unique solution. Therefore, we further employ the maximum entropy principle to develop a maximum entropy-least squares (MELS) model, which has a unique solution. To solve the MELS model, we develop a tailored augmented Lagrangian algorithm and conduct numerical studies on different transportation networks (i.e., a two-link single-OD network, the Sioux-Falls network and a real-world regional transportation network). The proposed approach is able to provide a rapid post-disruption evaluation of the overall link capacity loss in transportation network under limited information, i.e., without OD demand information and with limited information on link travel time.