The diode changes its own resistance, to create a voltage drop.
At 10 mA the voltage drop might be 0.6V.
At 1 A it might be 0.8V
If you measure current and voltage during the time it's conducting, then you can calculate power loss.
Taking an average reading is okay, although the results may be incorrect on account of dead time during the cycle. That is why you should try to get the reading for the time the diode is conducting.
A similar concept can be used to measure power lost by the mosfet.