In semantic communications, only task-relevant information is transmitted, yielding significant performance gains over conventional communications. To satisfy user requirements for different tasks, we investigate the semantic-aware resource allocation in a multi-cell network for serving multiple tasks in this paper. First, semantic entropy is defined and quantified to measure the semantic information for different tasks. Then, we develop a novel quality-of-experience (QoE) model to formulate the semantic-aware resource allocation problem in terms of semantic compression, channel assignment, and transmit power allocation. To solve the formulated problem, we first decouple it into two subproblems. The first one is to optimize semantic compression with given channel assignment and power allocation results, which is solved by a developed deep Q-network (DQN) based method. The second one is to optimize the channel assignment and transmit power, which is modeled as a many-to-one matching game and solved by a proposed low-complexity matching algorithm. Simulation results validate the effectiveness and superiority of the proposed semantic-aware resource allocation method, as well as its compatibility with conventional and semantic communications.