There are several words in English to denote the state of not being happy. Unhappy, irritated, angry, annoyed, unsatisfied, and dissatisfied etc. are a few words which denote this feeling.
But when it comes to dissatsified and unsatisfied, the meaning is different and it shall not be used interchangebly. Both are right usages but the meaning differs.The difference between dissatisfied and unsatisfied is subtle and hence you need to use these terms carefully.
Dissatisfied is a state of being annoyed / upset with something. A person might be dissatisfied by a lack of desired results, or by poor performance on a test.
Unsatisfied is a negation of the adjective satisfied (Satisfied means means fulfilled or content). To be unsatisfied is simply to be less than fully satisfied.
Example
If a meal is filling but tastes bad, you might say it is dissatisfying
If a meal tastes great but you are still hungry afterwards, it was unsatisfying