A few days ago I accidentally locked my closet door and had a most difficult time opening it without a key. I went online to find out how other people in similar situations managed to solve this most perplexing problem. There were plenty of suggestions to try, from sticking a hairpin in a small hole in the stem of the doorknob to removing the hinges from the door. None of them worked in my case. Then it dawned on me that even though the door was locked, the latch on the side of the door can still move. Armed with this knowledge, I straightened out a wire coat hanger and bent it so I could feed it around the latch, like this:
From this point all it takes is some tugging on the wire hanger to force the latch aside. If that doesn’t work, you can use a knife to move the latch far enough out of the way for you to open the door. The knob mechanism will still be locked, so remember to unlock it after the door opens, otherwise you’ll have to start this procedure all over again should you mark your triumph with a celebratory slam of the door.
MJBDiver.com 
Umm….did you try a credit card? Those usually work on that type of door. It looks as though it takes a key, did you try your house key? I used to jimmy open doors with a knife blade as well, just for fun mind you, not that I ever broke into a locked building or anything. LOL