That is how the circuit works.
A forward biased silicon diode limits the voltage to about 0.7V across it at your fairly low current. When the current is much higher then the diode limits the voltage to about 1V.
You can add an opamp circuit to limit the rectifier error to almost nothing but the output current is low. This opamp does not show its positive and negative power supply. Reverse the diodes for a negative output voltage.View attachment 42119