Voltage drop regulator 12 V to 5 V, voltage reference with zener diodes
If you observe the datasheet, you would find the appropriate working conditions where zener diode provides 3.3V drop across it on reverse breakdown. Just observe the below image from the datasheet. Bottom curve shows for 3.3V.

Closely looking at the given values, maximum voltage drop it would observe is 2.9V at 1mA current flow.

And the op-amp that you used, generally have input currents in the range of µA. That would mean the voltage across zener diode goes even low. From the result you posted. 5.56/3 = 1.85V drop is there.
For proper 3.3V. appropriate amount of current should flow through the diode.
Try looking at datasheet for in-depth reference.
Solution: Try putting pull-down resistor at opamp input(Proper value has to be selected).