It definitely depends on the season.
After Romo went down in 2015 I knew we were doomed so everything after that was "meh" for me. I had a small, SMALL, source of hope inside of me but it was quickly shattered with Weeden.
Our 2016 run losses didn't hurt as much because not only were they few and far between but you have to expect a few bumps a long the way.
However, if we lose an important game or a close game we should have won, yeah, it can tend to bother me (for a few days). What is funny is my wife knows it. I can walk in the house and she instanly picks up on my energy, "Cowboys lost eh?" or "Looks like the Boys won"? haha, yup.