In modern heterogeneous MPSoCs, the management of shared memory resources is crucial in delivering end-to-end QoS. Previous frameworks have either focused on singular QoS targets or the allocation of partitionable resources among CPU applications at relatively slow timescales. However, heterogeneous MPSoCs typically require instant response from the memory system where most resources cannot be partitioned. Moreover, the health of different cores in a heterogeneous MPSoC is often measured by diverse performance objectives. In this work, we propose a Self-Aware Resource Allocation (SARA) framework for heterogeneous MPSoCs. Priority-based adaptation allows cores to use different target performance and self-monitor their own intrinsic health. In response, the system allocates non-partitionable resources based on priorities. The proposed framework meets a diverse range of QoS demands from heterogeneous cores.