In one embodiment, a processor includes: a plurality of cores, at least some having an advanced programmable interrupt controller (APIC) identifier associated therewith; a plurality of power management agents associated with the plurality of cores; and a power controller to receive an indication of an interrupt and a first APIC identifier and send a wake signal and the first APIC identifier to the plurality of power management agents to determine which of the plurality of cores is associated with the first APIC identifier. Other embodiments are described and claimed.