Depressed is when someone is not angry or frustrated; it's more like when someone has stopped hoping something will happen and is just sad.
"He was depressed because he couldn't find a job, so he just sat on his couch and stared at the TV every day."
"I was depressed because my girlfriend left me, so I just lay in bed all day."
Upset is much more emotive. It's a bit like depressed, but with anger thrown in.
"He was so upset because he couldn't find a job that he threw a chair across the room."
"I was upset because my girlfriend left me, so I kicked the wall and put a huge hole in it."
Hope this helps. :)