Protein function prediction has long been a significant challenge in protein bioinformatics. Protein domains, as the structural and functional units, carry strong functional signatures. However, the vast number of domains and the limited availability of functional annotations introduce the issues of high dimensionality and sparsity when developing in-silico protein function prediction methods. To address these challenges, we have developed Domain-PFP, which leverages self-supervised learning to generate functionally aware representations of protein domains, effectively overcoming these limitations. By employing a lightweight shallow neural network, Domain-PFP captures the associations and co-occurrence relationships between protein domains and Gene Ontology (GO) terms, resulting in functionally informative domain embeddings. These embeddings demonstrate substantial functional relevance, as confirmed by multiple assessments, and are highly competitive in protein function prediction, outperforming current state-of-the-art methods. Additionally, we have created a Google Colab web service for Domain-PFP, allowing users to analyze domain-GO co-occurrence likelihoods, extract functionally aware protein representations, and predict protein functions through a user-friendly interface.