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The intrinsic magnetic topological insulator MnBi₂Te₄ has attracted significant interest recently as a promising platform for exploring exotic quantum phenomena. Here we report that when atomically thin MnBi₂Te₄ is deposited on a substrate such as silicon oxide or gold, there is a very strong mechanical coupling between the atomic layer and the supporting substrate. Considering that the layer number is a critical variant for the nontrivial phases in MnBi₂Te₄, we also investigate the layer dependence of lattice vibrations in MnBi₂Te₄. By measuring the circularly polarized Raman spectra of 1-11 layers MnBi₂Te₄, we observe that the interlayer breathing modes exhibit blueshift while the intralayer Raman modes show redshift for thinner samples. In addition, we also investigate the degradation in MnBi₂Te₄ thin layers by Raman spectroscopy, and find that low-energy Raman features are very sensitive to air exposure. Our work provides a convenient path to identify the layer number and sample quality of MnBi₂Te₄.