Being able to deal with punishments, even those perceived as unjust, with calm and grace is a generally useful and effective skill.
The correct approach is to realize that the person who suspended you did so for reasons that they believe are valid, and to express your disagreement in a calm and open-minded way, realizing that you may still be in the wrong (and that it is OK to be in the wrong; it happens).
One way to appeal a suspension that you believe is incorrect is to clearly and maturely state your case to the team in private, and move on from there. There is some related information here.
I strongly recommend that you wait a few days before sending off an email to the team. There is no real urgency here, and it will be to your benefit to cool down some. You will be able to make a stronger case if you do.