Why does an OpAmp with negative Feedback not amplify the potential difference on his inputs?
Let me answer with a simple numeric example.


Open-loop gain (inverting) of the opamp Aol=-10³=-1000
Feedback resistors R2=10k and R1=1k (Design goal: Closed-loop gain Acl=-10).
Real closed-loop gain (taking Aol into account): 

Acl=-[10/(1+10)]/[1/(1+10)+0.001]=-9.89

Comment: This equation results from the classical feedback formula.
Hence, for an input voltage of 1V the output voltage is -9.89V and the diff. voltage between both opamp inputs is 

Vdiff=-9.89/-1000=9.89 mV.
Of course, when the open-loop gain is larger, the closed-loop gain is much closer to the design goal and the diff. voltage is much smaller (µV range) and can be neglected (assumed to be zero for calculation purposes).

For an ideal opamp (Aol>>infinite): Acl=-(10/11)/(1/11)=-10