An accurate estimation of critical load levels (CLLs) is beneficial in evaluating the confidence level for the predicted locational marginal prices (LMPs) in power markets. This paper proposes an efficient algorithm to quickly identify CLLs under the with-loss-DCOPF framework. The proposed method approximates the trajectory of DCOPF solutions with respect to the system load variations. The quadratic coefficients of the trajectory can be efficiently obtained by solving a small-scale nonlinear system of equations formed by the variable substitution method, which does not require additional OPF runs and is thus more computationally efficient than existing methods such as binary search and interpolation. The obtained trajectory can be used for a quick calculation of OPF solutions without re-running OPF. Further, through trajectory extrapolation, new congestions and other binding constraints can be identified simultaneously with the CLL predictions. Particularly, the proposed method is not restricted to a specific DCOPF-based model and can be easily applied to other DCOPF-based variants. Numeric studies on a revised IEEE 30-bus system are presented to illustrate the high computational efficiency and accuracy of the approach. It is further tested on the IEEE 118-bus system using four different DCOPF-based models to illustrate its model adaptability.