There's a difference between standing up for yourself, and dropping to their levels. If you're -that- bothered and unable to just ignore it, then yes, the problem is yours, sadly. I'm not saying they've done nothing wrong, but in being an adult, you have to take crap and just shrug it off. It's the inevitability of being a parent, you have to take a lot of crap from your kids and you can't just holler at them and call them little bleeps that bleep their own bleep bleep bleep.
I mean... you can... but you're doing it wrong...
If you're doing your negativity, or whatever you call it, in post-game only, and barely if talking at all during game, then you have to really stop and consider what you're about to say. "Am I being positive, or at least neutral?" "Is this statement negative, am I calling someone a name?" "Is this passive-aggressive and questionably negative?" In post-game, you have all the time in the world. Just quit the game and leave the post-game chat. As Thumper so eloquently put it, "if you can't say something nice, don't say anything at all."
Furthermore, you never get chat-banned for one game... unless you showed extreme negativity or racist remarks. There's a trend when you get chat-banned, usually, so you need to think long and hard on the chat logs you've been provided, and look into what you're doing wrong, not assuming everyone else is wrong. Sometimes, you'll only get a chat log for one game, but I do not believe this to be a very common case.