Shitty feelings are exactly that, so for the most part I opt to not feel them. Which sounds like I'm burying the negative beneath a thin, and ultimately unstable veneer, but those who know me know that isn't the case. I think you can address and deal with something that has a negative impact without getting swept up in the emotional tide.
It helps that I have a strong desire to not bullshit myself, and an overwhelmingly realistic approach to life. Because of this, I'm not often surprised by things that happen. Most of the time I'm pretty aware of all possibilities and try not to hold myself to any one in particular. When something bad does happen, I feel more of an "oh, well I knew it was possible," more than a "that sucks."
It also helps me fix problems that crop up, getting to the root of what is making mad, sad, etc. If I'm not distracted by the feelings, I'm focused on what will get results.