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We investigate quantum phase transitions (QPTs) in various spin chain systems using the multipartite entanglement measure $\tau_\mathrm{SEF}$ based on the monogamy inequality of squared entanglement of formation (EOF). Our results demonstrate that $\tau_\mathrm{SEF}$ is more effective and reliable than bipartite entanglement or bipartite correlation measures such as EOF, von Neumann entropy, and quantum discord in characterizing QPTs. $\tau_\mathrm{SEF}$ not only detects critical points that may go unnoticed by other detectors but also avoids the issue of singularity at non-critical points encountered by other measures. Furthermore, by applying $\tau_\mathrm{SEF}$ , we have obtained the phase diagram for the XY spin chain with three and four interactions and discovered a new quantum phase.