Modern music streaming services are heavily based on recommendation engines to serve content to users. Sequential recommendation -- continuously providing new items within a single session in a contextually coherent manner -- has been an emerging topic in current literature. User feedback -- a positive or negative response to the item presented -- is used to drive content recommendations by learning user preferences. We extend this idea to session-based recommendation to provide context-coherent music recommendations by modelling negative user feedback, i.e., skips, in the loss function. We propose a sequence-aware contrastive sub-task to structure item embeddings in session-based music recommendation, such that true next-positive items (ignoring skipped items) are structured closer in the session embedding space, while skipped tracks are structured farther away from all items in the session. This directly affects item rankings using a K-nearest-neighbors search for next-item recommendations, while also promoting the rank of the true next item. Experiments incorporating this task into SoTA methods for sequential item recommendation show consistent performance gains in terms of next-item hit rate, item ranking, and skip down-ranking on three music recommendation datasets, strongly benefiting from the increasing presence of user feedback.