Bitcoin relies on the internet, and the power of computers around the world to power the transactions and iner-workings of the BTC. If the internet "goes down", there will be nothing left to power the whole BTC process, causing it to breakdown.
You are right. But the chances for entire Internet goes into off-line is zero. Because Internet is not running from one single computer. Power shutdown is not possible for all over the world so internet will stay alive in some part of the world.