"Anastasia" is female name. So I believe this is a typo and you actually mean "anesthesia". And the state you asked about - "anesthesia" (same word) or "narcosis".

ps: not a native speaker

The word you mentioned, "anesthesia", can actually be used to describe the state. From wikipedia:

In the practice of medicine (especially surgery and dentistry), anesthesia or anaesthesia (from greek "without sensation") is a state of temporary induced loss of sensation or awareness.

You can also use the word "narcosis". From Collins:

unconsciousness induced by narcotics or general anaesthetics

Your example sentence could then be:

I was under anesthesia during the operation

or

I was in a state of narcosis during the operation