When a patient is given anesthesia, they go through three stages. During the first stage, the anesthesia is administered, and they may start to feel its effects but mildly. In the second stage they might feel some twitching or agitation. In the third stage, their muscles will relax, and they will go into unconsciousness. Usually, this is all that happens and nothing serious occurs.
In rare cases, there can be an overdose which can lead to heart failure as well as brain damage. Elderly people with Alzheimer’s or Parkinson’s disease, may have memory or learning problems as side effects of the anesthesia, but, in general, anesthesia does not negatively affect the brain of a healthy individual as long as it is being used correctly.
This is also true only for general anesthesia which results in completely unconscious. Regional and local anesthesia, for example, will not cause any problems with the brain since it only affects the nerves of one part of the body.