Multi-criteria (MC) recommender systems, which utilize MC rating information for recommendation, are increasingly widespread in various e-commerce domains. However, the MC recommendation using training-based collaborative filtering, requiring consideration of multiple ratings compared to single-criterion counterparts, often poses practical challenges in achieving state-of-the-art performance along with scalable model training. To solve this problem, we propose CA-GF, a training-free MC recommendation method, which is built upon criteria-aware graph filtering for efficient yet accurate MC recommendations. Specifically, first, we construct an item-item similarity graph using an MC user-expansion graph. Next, we design CA-GF composed of the following key components, including 1) criterion-specific graph filtering where the optimal filter for each criterion is found using various types of polynomial low-pass filters and 2) criteria preference-infused aggregation where the smoothed signals from each criterion are aggregated. We demonstrate that CA-GF is (a) efficient: providing the computational efficiency, offering the extremely fast runtime of less than 0.2 seconds even on the largest benchmark dataset, (b) accurate: outperforming benchmark MC recommendation methods, achieving substantial accuracy gains up to 24% compared to the best competitor, and (c) interpretable: providing interpretations for the contribution of each criterion to the model prediction based on visualizations.