How can I call in after denied promotion? Without looking bad?

I’ve been working towards a promotion for. Couple years. Have been pretty much doing the job already.. so messed up. They open the position, I apply go through a rigorous interview testing process.. all to be told I’m not being hired because of this skills test..I’m unqualified.. I think it’s totally office politics.. because if anything I’m overqualified for this “entree level position” which in reality is actually a step down from what I’m doing, it’s even a 10k paycut.. the whole thing is just SO insulting.. my college degree is in this field .. despite scoring 80% on the skills test it wasn’t “good enough”..and I truly need time to digest.. like a few days into this next week. I’m devastated. How unacceptable is it for me to ask for unpaid time off.. I have no vacation. They are total sticklers about time off.. and it was mentioned to me I need to still be “cool” if I want any chance at the job again.. I’ve already been passed over a couple times... and yeah I just can’t bring myself to be motivated at work after all that. How do I professionally and “cooly” ask for the time off that I need so that I can move past this and show back up next week with a better attitude ? Should I just make something up like my grandma passed away? Or be honest ?