Do I need to cite Mathematica in my paper?
I would recommend to always cite software that you use in your calculations (no need for LaTeX, obviously). 
A screw driver will always stay a screw driver, but software is a little bit more complex. 

Have you heard of the little bug that may invalidate 15 years of brain research? I think in that case it would be quite nice to know which version of the software you used. 

And in your case: can you really be sure that Mathematica has not a specific bug that you haven't noticed? In Version 10, I noticed that some linear-log plots were messed up and that was fixed in a later version 10.1. It could have easily happened that I had published a wrong graph, and thus I think it is quite important to give detailled information about the software that you use.