The diffuse Galactic $\gamma$-ray emission is produced from the interaction of cosmic rays and interstellar medium or radiation fields in the Galaxy, where neutrino production is also expected. Recently, the Large High Altitude Air Shower Observatory (LHAASO) reported the measurements of the diffuse $\gamma$-ray from the Galactic plane with energies above 10 TeV. In this study, we construct the neutrino emission template based on LHAASO's observation and search for diffuse neutrinos accompanying the LHAASO diffuse Galactic $\gamma$-ray emission using ten-year IceCube track events. No significant signals are found. We set 90\% confidence level upper limits, with the resulting neutrino flux being $\rm d\phi_\nu/\rm dE_\nu=1.27\times10^{-14}(E_{\nu}/25\mathrm{TeV})^{-2.99}\mathrm{TeV}^{-1}\mathrm{cm}^{-2}\mathrm{s}^{-1}$ for the diffuse $\gamma$-ray flux map with $1.5\sigma$ significance cut.