Adapting foundation models for specific purposes has become a standard approach to build machine learning systems for downstream applications. Yet, it is an open question which mechanisms take place during adaptation. Here we develop a new Sparse Autoencoder (SAE) for the CLIP vision transformer, named PatchSAE, to extract interpretable concepts at granular levels (e.g., shape, color, or semantics of an object) and their patch-wise spatial attributions. We explore how these concepts influence the model output in downstream image classification tasks and investigate how recent state-of-the-art prompt-based adaptation techniques change the association of model inputs to these concepts. While activations of concepts slightly change between adapted and non-adapted models, we find that the majority of gains on common adaptation tasks can be explained with the existing concepts already present in the non-adapted foundation model. This work provides a concrete framework to train and use SAEs for Vision Transformers and provides insights into explaining adaptation mechanisms.