There are usually two common culprits for this.
1. You need to check in your motherboard's BIOS for a setting that relates to what the power state will be set to after an AC power loss. The settings I'm familiar with are On / Off / Last State.
If set to On, your computer will power on whenever you plug it in, or anytime power has been lost and then restored, such as during an electrical outage.
If set to Off, your computer will remain off until you press the power button.
If set to Last State, it will turn on if your computer was on when power was lost, or remain off, if your computer was off when power was lost.
2. Devices attached in Windows can be set to wake the computer, such as a keyboard, mouse, or network card. Mice are very sensitive, and when set to wake the computer, often times will wake it when it's unintended. It's usually best to disable this wake feature on your mouse, turn off the mouse, or flip the mouse over so any movement is ignored.
If you start a CMD prompt (command prompt) in Windows, Windows Logo Key + R, type CMD in the run dialog, and click OK,you can query power management to find out which devices are set to wake the computer.
In the CMD prompt type powercfg /devicequery wake_armed and press Enter. Properly executed, this command will either return a list of devices that are able to wake the computer from sleep or it will simply return the word None.
Once you have a list of devices capable of waking the computer, the easiest way to change that behavior is through the Device Manager.
Still in the CMD prompt, type devmgmt.msc, press Enter, and the Device Manager will open.
Locate each device on the list returned by your powercfg query and double-click them to open their properties. In the properties dialog for your device, if it is capable of waking your computer, there will be a Power Management tab. Choose the Power Management tab and clear the Allow this device to wake the computer checkbox to remove the device from the list of devices which can wake the computer from sleep.