A long-standing dilemma prevents the broader application of explanation methods: general applicability and inference speed. On the one hand, existing model-agnostic explanation methods usually make minimal pre-assumptions about the prediction models to be explained. Still, they require additional queries to the model through propagation or back-propagation to approximate the models' behaviors, resulting in slow inference and hindering their use in time-sensitive tasks. On the other hand, various model-dependent explanations have been proposed that achieve low-cost, fast inference but at the expense of limiting their applicability to specific model structures. In this study, we bridge the gap between the universality of model-agnostic approaches and the efficiency of model-specific approaches by proposing a novel framework without assumptions on the prediction model's structures, achieving high efficiency during inference and allowing for real-time explanations. To achieve this, we first define explanations through a set of human-comprehensible concepts and propose a framework to elucidate model predictions via minimal feasible concept sets. Second, we show that a minimal feasible set generator can be learned as a companion explainer to the prediction model, generating explanations for predictions. Finally, we validate this framework by implementing a novel model-agnostic method that provides robust explanations while facilitating real-time inference. Our claims are substantiated by comprehensive experiments, highlighting the effectiveness and efficiency of our approach.