Asthma is an inflammatory disease of the lungs. When your lungs are inflamed, they produce a lot of thick, sticky mucus that is hard to move out of the lungs.
Normally, people with healthy lungs produce about a cup a day of thin, watery mucus to the back of the throat and swallow it without even realizing it. This is a little harder to do when you have asthma because of the consistency and amount of the mucus.
The mucus at the back of your throat may be caused by rhinitis (inflammation of the sinuses) that is many times linked with asthma.
Inhaled corticosteroids are the medication of choice in dealing with the inflammation. My recommendation is to see a doctor that specializes or has an interest in asthma or allergy management to get it under control ASAP.