So you wake up with a smudge on your pillow. Oops. The good news is that one night every now and then is not going to result in skin armageddon unless you have very sensitive skin.
However, you should mitigate the damage right away, by thoroughly washing your face and applying skin care products. This should stem off any breakouts and other immediate result of having accidentally snoozed with your face still covered. Wash your hands before doing so, in case your skin is damaged.
Then change out your pillowcase. If you're traveling in a hotel and don't want housekeeping to do a full clean, switch to one of the extra pillows. The pillowcase is going to need to be washed.
But the best thing to do is not go to sleep with makeup on in the first place. Make sure to do your night skin routine no matter how tired you are or how late it is, and keep those makeup remover wipes on your nightstand as a backup.