Let's consider a flat plate and let it fly both at subsonic and at supersonic speeds.
Let's start with the subsonic case and let's see how the airflow looks like around the flat plate (picture source)
At subsonic speed the airflow has enough time to move out of the way and "get around" the flat plate. As depicted in the picture, the airflow starts to bend well in front of the flat plate and basically all around and far from it. The bending of the streamlines generates a relevant pressure field (according to Bernoulli) which is always globally pointing upward i.e. it generates a total aerodynamic force which is always a pure lift. The fact that at subsonic speed no drag is generated around an aerodynamic body is called D'Alembert paradox.
Drag obviously does exist at subsonic speed and is mainly due to the fluid's viscosity but as a first approximation we can simply ignore it and live with the fact that the airflow "encircles" the aerodynamic body (our flat plate) generating a pure lift.
What happens now at the flat plate at supersonic speed? The flow is now so fast that it simply cannot realise the presence of the flat plate until it just crashes against its leading edge. At that point the flow suddenly changes its curvature to follow the flat plate's surface. And when it reaches the leading edge, it just changes (suddenly again) its curvature to become again parallel to the freestream (picture source):
Also at supersonic speed this sudden change in speed comes with a relevant change in pressure (lower on the upper surface; higher on the bottom) but this time the pressure acts everywhere perpendicular to the flat plate's surface i.e. it always possesses a component pointing backward: at supersonic speed, even considering an inviscid fluid, the aerodynamic force (R in the previous picture) is always composed by a lift and by a drag. This latter is called wave drag.
For that reason alone the same flat plate flying at supersonic speed generates a lower $C_l$ than at subsonic speed. Anyway at supersonic speed there's much more going on, with changes in density and temperature which cannot be neglected and which globally contributes to increasing dissipation and to reducing lift in respect to the subsonic case.