My coping mechanism involves an understanding of how “it’s just a game” is a simple misinterpretation of what a loss in Eve truly represents. Your ship at the very least represents the time spent on obtaining it, which may or may not be a big deal. Reflect on that before you undock. Only when you can promise yourself that you can emotionally deal with the worst case scenario (losing ship + getting podded) and aim to learn from it, you undock. If you don’t feel that way, you’re not in the right mindset to be playing EvE for the moment.
There’s no shame in walking away for a spell to recollect your thoughts. My best way? Smoke a cigarette (or just take a walk) outside. Reminds me the game is not that important. I feel a lot better when I detach from the screen for a few minutes, laughing at my own bruised gamer ego after I got my ass handed to me. Are you sure the emotion you are sensing is depression? I always feel a bit humiliated after a loss, and it’s okay to address this. To some this is reason to leave the game. For others like me, it is motivation to get better. It’s just a matter of mindset.