I would use these words in different ways.
I would call a man desperate if he were reckless and didn't care about the consequences.
For example, a thief might do something desperate if he thought he was about to be discovered.
He might shoot someone!
I would call a situation desperate if it were critical and there was an extreme need.
For example, going for weeks without rain, the farmers were desperate for rain.
I would use the word disappointed to describe someone who was frustrated.
For example, a student might be disappointed that they got 60% on a test when they were hoping for 70%.
I would use the word disappointed to describe a situation that failed but was not extreme.
For example, I was disappointed that it rained. I hoped to go to the beach, but maybe it will be sunny tomorrow.
Hope this helps