Gradual slowing breath, its effect on health
You can try as much to slow down your breathing but the body will speed it up if it requires. What you've probably done is relaxed and just basically meditated. It's not the breathing but the relaxing yourself to slow your breathing and the focus which has refreshed you. I say conduct some experiments, like listen to calming music and relax and don't monitor your breathing and see if you feel the same. 

//updating answer

Slowing your breathing builds up the carbon dioxide in your body. This is bad for the body so it forces you to breathe. In fact our breathing is seriously tightly controlled so that our body tightly controls the carbon dioxide (or more correctly the pH) in our blood. There are some groups of patients in which permanent slow breathing exists. In these people their carbon dioxide climbs and the kidneys have to compensate.