You can play soccer and have asthma. First off I don't have asthma but I did have it mildly as a kid, and I play soccer and after sprinting even 50 yards sometimes I am out of breath (and I am pretty fit.) It is normal to be breathless feeling in the sport, since fitness is a HUGE component of soccer. I know a few women with inhalers that play, I see them puff the inhaler on the sideline. Anyways, I bet a lot of the out of breathness is just since you are running. I've noticed if you sprint at 100% you will fatigue very fast, you can even get sick. You should train (do slow jogs, and fast interval work on your own). Asthma isn't going to be a help, but it shouldn't be such a burden thta you cant play.
Tell your team you have asthma, and talk to your Dr about hwo to best go about things. I wouldn't think they'll be mad at you if you need to sub out due to an asthma attack!!! Don't worry about that stuff, playing sports is about having fun and working out.