My iphone 5 battery is draining too fast?

So i want to know if you think it was my mistake cause i bought it on friday and i was marveled because the battery life was so excellent. Today i went to school and forgot to unplug my phone from the charger and i used it 20 minutes and battery was down by 20 percent, Was it my fault? I always left plugged my iphone 4s and battery was way better than my 5? Any person experiencing this problem?

Weird that it would go down so fast. Maybe you didn't initially charge it like you thought you did? If you were running video on it the battery would go out super fast. There are ways to increase battery life too like turning off location services, turning brightness down, turning off wi-fi when you are roaming.

Keeping your iPhone charging for longer than it needs to, just like any battery, will decrease the usage time you will get from it. Try running it through a few cycles of letting it drain to about 5%, charging it up to 100%, and then repeat for a few days. If it's still not working, your battery may be damaged. Considering your iPhone is very new, Apple will replace the battery for free if it is broken, so bring it down to the Genius Bar. Also, avoid unplugging your phone before it reaches its 100% charge, and leave it plugged in for just about 10 mins after it gets to that point.

Turn off Wi-Fi, BlueTooth, location services you don't need all the time. Reduce Screen Brightness
Settings---Brightness---Put the slider to about 1/4 mark or lower.
Turn off Auto Brightness
Settings---Brightness---Turn off Auto Brightness
Turn off Location
Settings--General--Location Services---Click on the top option to disable all location services
Turn off Push Email
Settings--Mail, Contacts, Calendar--Choose Fetch New Data and Slide to Off
Fetch Less Often
Settings--Mail, Contacts, Calendar--Select Fetch New Data---Choose Either an Hour or Manually Auto Lock Sooner:
Settings--General--Auto Lock--Select 1 Minute