In real-time systems that employ preemptive scheduling and cache architecture, it is essential to account as precisely as possible for cache-related preemption delays in the schedulability analysis, as an imprecise estimation may falsely deem the system unschedulable. In the current state of the art for preemptive scheduling of tasks with fixed preemption points, the existing schedulability analysis considers overly pessimistic estimation of cache-related preemption delay, which eventually leads to overly pessimistic schedulability results. In this paper, we propose a novel response time analysis for real-time tasks with fixed preemption points, accounting for a more precise estimation of cache-related preemption delays. The evaluation shows that the proposed analysis significantly dominates the existing approach by being able to always identify more schedulable tasksets.