Cache compression is a promising technique to increase on-chip cache capacity and to decrease off-chip bandwidth usage. While prior compression techniques always consider a trade-off between compression ratio and decompression latency, they are oblivious to the variation in criticality of different cache blocks. In multi-core processors, last-level cache (LLC) is logically shared but physically distributed among cores. In this work, we demonstrate that, cache blocks within such nonuniform architecture exhibit different sensitivity to the access latency. Owing to this behavior, we propose a criticality-aware compressed LLC that favors lower latency over higher capacity based on the criticality of the data blocks. Based on our studies on a 16-core processor with 4MB LLC, our proposed criticality-aware mechanism improves the system performance comparable to that of with an 8MB uncompressed LLC.