By performing resonant inelastic x-ray scattering (RIXS) measurements at the Ir $\mathit{L_{\mathrm{3}}}$ edge, we have investigated the low-energy elementary excitations in a series of double perovskite iridate single crystals, La$_{2}$$\mathit{M}$IrO$_{6}$ ($\mathit{M}$ = Co, Ni, and Zn). Almost dispersionless magnetic excitations at $\sim$ 42(6) meV and $\sim$ 35(5) meV have been observed in crystals containing magnetic 3$\mathit{d}$ ions, La$_{2}$CoIrO$_{6}$ and La$_{2}$NiIrO$_{6}$, respectively. In contrast, this low-energy magnetic excitation is absent in La$_{2}$ZnIrO$_{6}$ in which the 3$\mathit{d}$ ions are non-magnetic, suggesting the importance of 3$\mathit{d}$-5$\mathit{d}$ hybridization in the magnetic properties of these double perovskite iridates. The magnetic excitation is suppressed completely above the magnetic ordering temperature, suggesting the inadequacy of using a simple spin Hamiltonian to describe magnetism of these materials.