Learning high-quality, robust, efficient, and disentangled representations is a central challenge in artificial intelligence (AI). Deep metric learning frameworks tackle this challenge primarily using architectural and optimization constraints. Here, we introduce a third approach that instead relies on $\textit{functional}$ constraints. Specifically, we present MonoCon, a simple framework that uses a small monotonic multi-layer perceptron (MLP) head attached to any pre-trained encoder. Due to co-adaptation between encoder and head guided by contrastive loss and monotonicity constraints, MonoCon learns robust, disentangled, and highly compact embeddings at a practically negligible performance cost. On the CIFAR-100 image classification task, MonoCon yields representations that are nearly 9x more compact and 1.5x more robust than the fine-tuned encoder baseline, while retaining 99\% of the baseline's 5-NN classification accuracy. We also report a 3.4x more compact and 1.4x more robust representation on an SNLI sentence similarity task for a marginal reduction in the STSb score, establishing MonoCon as a general domain-agnostic framework. Crucially, these robust, ultra-compact representations learned via functional constraints offer a unified solution to critical challenges in disparate contexts ranging from edge computing to cloud-scale retrieval.