The Arduino Nano accepts the 7-12 Volt input power not from the USB port, but from the Vin pin (pin30), see the diagram below:
If you want to supply regulated power, then a 5 Volt regulated adapter needs to feed the +5V pin (pin27) instead.
From the official Arduino Nano page:
Power:
The Arduino Nano can be powered via the Mini-B USB connection, 6-20V unregulated external power supply (pin 30), or 5V regulated external power supply (pin 27). The power source is automatically selected to the highest voltage source.
The FTDI FT232RL chip on the Nano is only powered if the board is being powered over USB. As a result, when running on external (non-USB) power, the 3.3V output (which is supplied by the FTDI chip) is not available and the RX and TX LEDs will flicker if digital pins 0 or 1 are high.