In this paper, we propose an algorithm for Context-Aware REgulation of backoff delay (d-CARE) in delay-sensitive networks that follow IEEE 802.15.4 standard. The slotted Carrier Sense Multiple Access - Collision Avoidance (CSMA-CA) algorithm prescribed in the standard, to resolve the contention over channel access, does not select the initial Backoff Exponent (BE) value judiciously. In other words, it cannot differentiate between delay-sensitive and delay-tolerant applications. Thus, context-less selection of BE may lead towards a high delay for delay-sensitive applications, for example - real time health monitoring of patients. The proposed d-CARE algorithm uses a Fuzzy Inference System (FIS) to address this problem. As a case study, contexts or attributes that are relevant to healthcare applications are considered as the inputs to the FIS, which generates a BE value as the corresponding output. This judiciously selected BE value produces 12% less delay than the traditional approach.