If you use Instantiate to create the ParticleSystem when the button is pressed, it will have created a clone in your hierarchy window. You will need to use Destroy to eliminate the clone that was instantiated. One way to do this, would be to attach a script to the gameObject of the ParticleSystem, that does a StartCoroutine in which you will WaitForSeconds (long enough for the Particle to complete), and then Destroy(transform.gameObject);. The script would look something like:

void Start() {StartCoroutine(DestroyClone());}
IEnumerator DestroyClone() {yield return new WaitForSeconds(5);Destroy(transform.gameObject);}

This assumes 5 seconds is sufficient for your particlesystem to complete. The script would be attached to your ParticleSystem's gameobject.