Clustering algorithms rely on complex optimisation processes that may be difficult to comprehend, especially for individuals who lack technical expertise. While many explainable artificial intelligence techniques exist for supervised machine learning, unsupervised learning -- and clustering in particular -- has been largely neglected. To complicate matters further, the notion of a ``true'' cluster is inherently challenging to define. These facets of unsupervised learning and its explainability make it difficult to foster trust in such methods and curtail their adoption. To address these challenges, we propose a new, model-agnostic technique for explaining clustering algorithms with counterfactual statements. Our approach relies on a novel soft-scoring method that captures the spatial information utilised by clustering models. It builds upon a state-of-the-art Bayesian counterfactual generator for supervised learning to deliver high-quality explanations. We evaluate its performance on five datasets and two clustering algorithms, and demonstrate that introducing soft scores to guide counterfactual search significantly improves the results.