You can use a via for your purpose. It is probably the power planes are internal. Use a via to connect from the signal planes to the internal power or ground plane.

Using a via can make connection with ground plane.In case of surface-mount component, there is separate via connected to the surface-mount pad. In case of throughole component, the pin is soldered into the via.

If you put a big copper plane for ground on layer 2 and another one for power on 3 and assign them to the ground and power nets respectively. When you glood the copper, PADS will connect them as you want.