Automatic keyword extraction (AKE) has gained more importance with the increasing amount of digital textual data that modern computing systems process. It has various applications in information retrieval (IR) and natural language processing (NLP), including text summarisation, topic analysis and document indexing. This paper proposes a simple but effective post-processing-based universal approach to improve the performance of any AKE methods, via an enhanced level of semantic-awareness supported by PoS-tagging. To demonstrate the performance of the proposed approach, we considered word types retrieved from a PoS-tagging step and two representative sources of semantic information - specialised terms defined in one or more context-dependent thesauri, and named entities in Wikipedia. The above three steps can be simply added to the end of any AKE methods as part of a post-processor, which simply re-evaluate all candidate keywords following some context-specific and semantic-aware criteria. For five state-of-the-art (SOTA) AKE methods, our experimental results with 17 selected datasets showed that the proposed approach improved their performances both consistently (up to 100% in terms of improved cases) and significantly (between 10.2% and 53.8%, with an average of 25.8%, in terms of F1-score and across all five methods), especially when all the three enhancement steps are used. Our results have profound implications considering the ease to apply our proposed approach to any AKE methods and to further extend it.