Virtual particles are basically just a mathematical trick to make doing calculations easier in perturbative quantum field theory. You shouldn't take them too seriously.

If you do the calculations in another way (e.g. by discretizing stuff on a lattice) no virtual particles appear but your calculations become a lot harder.

They don't just become harder, they become open problems -- open problems with a million dollar bounty on them! There is no known non-perturbative quantization of the Yang-Mills theory.

http://www.claymath.org/millennium-problems/yang–mills-and-m...

They are still a trick because they are used to propagate a particle exactly where it needs to go in order to exert the force of the field. So the field is everywhere, but is pretty much invisible except for when virtual particles mediate it.. No efficient simulation on a computer could operate in such a manner. It's explanatory but not a constructive proof. I can't build an efficient simulation of our universe based on the virtual particle paradigm.