Do you normally wake up from general anesthesia feeling disoriented?

Typically: It is not uncommon to immediately wake up after a general anesthetic and need to be reminded a few times of your orientation by the recovery room nurse. The action of an anesthetic is to block memory during surgery so as it wears off, your memory returns over time ( albeit short) and you need a few reminders. No worries.

Was it long lasting?: If you remember being very disoriented after waking up from anesthesia, and it is troubling, it is reasonable to contact your anesthesiologist and find out if they were aware of your perceived disorientation and whether you had an unusual reaction to medication. This information will also help you be prepared for a future surgery.

Initially Yes.: The chemical that we use to induce general anesthesia act on the whole brain. Because of this it takes some time for the person to come clearly awake, frequently people are somewhat disoriented in the immediate post-operative period. This usually clears very quickly.