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In this paper, we propose an approach to estimate the worst-case response time (WCRT) of each task in a preemptive multitasking single-processor real-time system utilizing an L1 cache. The approach combines intertask cache-eviction analysis and intratask cache-access analysis to estimate the number of cache lines that can possibly be evicted by the preempting task and also be accessed again by the preempted task after preemptions (thus requiring the preempted task to reload the cache line(s)). This cache-reload delay caused by preempting task(s) is then incorporated into WCRT analysis. Three sets of applications with up to six concurrent tasks running are used to test our approach. The experimental results show that our approach can tighten the WCRT estimate by up to 32% (1.4X) over prior state-of-the-art.