Adding a light fixture to an existing fixture
The method for adding a new light fixture to come on when the old one does is this: You do not disconnect any of the existing wires (except temporarily while working on it). You add wires only, connecting one screw on the old fixture to one screw on the new fixture, and the other screw on the old fixture to the other screw on the new fixture. This is called connecting the fixtures in parallel. Any method that does not connect the fixtures in parallel will not work. 

Now -- exactly how you connect these screws together depends on what your fixtures look like, where power is supplied to the old light circuit (at the fixture or at the switch), and where (in what country and state) you live.

I strongly recommend that you continue to communicate on this site until you have a complete answer to your question, before doing any more work on your electrics. Judging by the mistake you describe, if you continue without guidance you may do much worse than make something that doesn't work properly. You may hurt yourself or damage your residence.