The internet isn't just one physical point on Earth, it's a centralized system of communication. You can't just "shut down the internet", unless in the case of some EMP or nuclear apocalypse, which will pose more problems than simply Bitcoin
If the internet was actually centralized then it could be disconnected by attacking the central authority that controls the internet. The internet however is not centralized and cannot be shut down as no one entity controls the internet. If a major provider of internet service (either an ISP or a service that provides the "backbone" of the internet) were to be shut down because of an attack or otherwise then other service providers would be able to pick up the slack
That was a typo, I meant to say it's NOT a centralized system of communication. The rest of my statement supports that.
I would say that even an EMP attack would not be able to shut down the entire internet (unless the attack spread throughout the entire world) as an EMP attack would simply shut down part of the internet but other parts would be able to pick up the slack.