No. The console, like your TV and most of your electronics without a physical power switch, including your computer (that is why some computers power supplies have a physical power switch), your system is only in a standby state. This allows you to have a button press turn on action. In other words you can press the power button your TV remote to turn on the TV, you can press a button on the computer to turn it on, and not have a physical switch like the old days of computers, TVs (before your and my time... I am talking about TV without Remote Controls or early days of Remotes which only had channel change and volume, and not on/off state) and so on.
I guess you can see the different power states of a typical consumer product as the following, which may or may not support:
Physically turned off (this includes the device unplugged from its power source)
Modern game console supports: State 1 (unplugging the console from the wall), State 3 which is what you did, and is identified as "power down" on the console, but not truly is, State 4 and of course State 5.
An old school console like the Super Nintendo or GameCube, supports State 1 and 5 only. (on and off, notice how the power switch, switches states, either it slides like a sliding switch of 2 states, or the button remains pressed in when you press it, and return to it's normal height when pressed again).