Network Function Virtualization (NFV) has paved the way for the migration of Virtual Network Functions (VNFs) into multi-tenant datacenters, lowering the barrier for the introduction of new processing functionality into the network. Recent trends for resource orchestration across the entire compute continuum raise the need for decision making at low timescales, a requirement which can be hardly met by centralized resource optimizers that rely either on Linear Programming or Machine Learning (ML). In this respect, we present a distributed approach tailored to a crucial resource orchestration aspect, i.e., the embedding of Service Function Chains (SFCs) onto large-scale virtualized network infrastructures. In order to confront the computational hardness of the SFC embedding problem, we utilize a clustering method for the partitioning of the solution space, empowering the search for efficient solutions in parallel across all clusters. Another salient feature of our approach is the use of unsupervised deep learning for the computation of embeddings within each cluster. Our distributed SFC embedding framework is benchmarked against a state-of-the-art heuristic and a distributed greedy algorithm. Our evaluation results uncover notable gains in terms of resource efficiency, combined with solver runtimes in the order of milliseconds with thousands of substrate nodes.