Evaporated α-spectra have been measured in coincidence with low energy discrete γ-rays from residual nucleus $^{68}$Zn populated by αn evaporation from compound nucleus $^{73}$Ge produced in the reaction $^{64}$Ni($^{9}$Be,αn)$^{68}$Zn at $E({}^9$Be) = 30 MeV. Low energy γ-gated α-particle spectra, for the first time, have been used to extract the nuclear level density (NLD) for the intermediate $^{69}$Zn nucleus in the excitation energy range of E ≈ 4-20 MeV. The slope of present NLD data as a function of excitation energy for $^{69}$Zn matches nicely with the slope determined from RIPL estimates for NLD at low energies and the NLD from neutron resonance data at neutron separation energy $S_n$. The extracted inverse NLD parameter (k = A/$\tilde{a}$) has been used to determine the nuclear level density parameter value a at neutron separation energy $S_n$ for $^{69}$Zn. The cross section of $^{68}$Zn(n,γ) capture reaction as a function of neutron energy is then estimated employing the derived $a\left(S_n\right)$ in the reaction code TALYS. It is found that the estimated neutron capture cross section agrees well with the available experimental data without any normalization. The present result indicates that experimentally derived nuclear level density parameter can constrain the statistical model description of astrophysical capture cross section and optimize the uncertainties associated with astrophysical reaction rate.