Graph neural network (GNN)-based models have been extensively studied for recommendations, as they can extract high-order collaborative signals accurately which is required for high-quality recommender systems. However, they neglect the valuable information gained through negative feedback in two aspects: (1) different users might hold opposite feedback on the same item, which hampers optimal information propagation in GNNs, and (2) even when an item vastly deviates from users' preferences, they might still choose it and provide a negative rating. In this paper, we propose a negative feedback-aware recommender model (NFARec) that maximizes the leverage of negative feedback. To transfer information to multi-hop neighbors along an optimal path effectively, NFARec adopts a feedback-aware correlation that guides hypergraph convolutions (HGCs) to learn users' structural representations. Moreover, NFARec incorporates an auxiliary task - predicting the feedback sentiment polarity (i.e., positive or negative) of the next interaction - based on the Transformer Hawkes Process. The task is beneficial for understanding users by learning the sentiment expressed in their previous sequential feedback patterns and predicting future interactions. Extensive experiments demonstrate that NFARec outperforms competitive baselines. Our source code and data are released at https://github.com/WangXFng/NFARec.