By transmitting task-related information only, semantic communications yield significant performance gains over conventional communications. However, the lack of mature semantic theory about semantic information quantification and performance evaluation makes it challenging to perform resource allocation for semantic communications, especially when multiple tasks coexist in the network. To cope with this challenge, we propose a quality-of-experience (QoE) based semantic-aware resource allocation method for multi-task networks in this paper. First, semantic entropy is defined to quantify the semantic information for different tasks, and the relationship between semantic entropy and Shannon entropy is analyzed. Then, we develop a novel QoE model to formulate the semantic-aware resource allocation in terms of semantic compression, channel assignment, and transmit power. The compatibility of the formulated problem with conventional communications is further demonstrated. To solve this problem, we decouple it into two subproblems and solved them by a developed deep Q-network (DQN) based method and a proposed low-complexity matching algorithm, respectively. Finally, simulation results validate the effectiveness and superiority of the proposed method, as well as its compatibility with conventional communications.