I think most of the veterans here will tell you that you waited too long to whack the coach. Personally, my typical process is to allow him the initial reaction without saying much, unless he is WAY out of line. The next time he brings it up, he gets the warning. The third time, he gets stuck.
Your partners, who allowed him to gripe that you are too sensitive, have no guts.
You were fine in the manner in which you dealt with the coach. My only suggestion is you need to casually mention to your partners that you posted the sitch on this site, so they can get the message as well.