Recently, the pressure has been used as external stimuli to induce structural and magnetic phase transitions in many layered quantum materials whose layers are linked by van der Waals forces. Such materials with weakly held layers allow relatively easy manipulation of the superexchange mechanism and lead to novel magnetic behavior. Using the hydrostatic pressure as a disorderless means to manipulate the interlayer coupling, we applied pressure on two quasi-2D sister compounds, namely, Cr2Si2Te6 (CST) and Mn3Si2Te6 (MST), up to ~1 GPa. Magnetic property measurements with the application of pressure revealed that the ferromagnetic transition temperature decreases in CST while the opposite trend occurs for the ferrimagnet MST. In MST, the magnetization decreases with the increase in the pressure, and such trend is not clearly noticed in CST, within the pressure range studied. Theoretical calculations showed the overall pressure effect on layer separation, bond angle, and exchange coupling, strongly influencing the change in subsequent magnetic characteristics. Exchange coupling in Mn3Si2Te6 is strongly frustrated and the first nearest neighbor interaction is the most dominant of the components with the strongest pressure dependence. Whereas, in Cr2Si2Te6, the exchange coupling parameters exhibit very little dependence on the pressure. This combined experimental and theoretical work has the potential to expand to other relevant quantum materials.