I was working on completing Hastur's Finding the Way mystery when Hastur woke up and the character with the key had a blight and died therefore devoured. I played it like I lost the game because when a character is usually devoured you lose all their stuff. Did I play that right?

Depends. What was the mechanism whereby the character gained the key? I don't have the mystery in front of me, but if it's something like other mysteries (when a character gains an artifact they can instead gain "artifact x"), then you may still be able to reacquire the key. On the other hand, the likelihood of getting this done in time when Hastur is awake is pretty low.

Depends. What was the mechanism whereby the character gained the key? I don't have the mystery in front of me, but if it's something like other mysteries (when a character gains an artifact they can instead gain "artifact x"), then you may still be able to reacquire the key. On the other hand, the likelihood of getting this done in time when Hastur is awake is pretty low.

The card text reads After an investigator resolves a research encounter he places the token on the card. If there are tokens equal to the number of investigators he gains the artifact. However, a character who had the artifact was devoured and therefore it is permanently gone right?

The rules for devoured just state that you discard their possessions, its only the investigator that is returned to the box. So I'd say that the next time an investigator resolves a research encounter and places a token on the mystery the key can be "rediscovered".

"After an Investigator resolves a Research Encounter, he may spend 1 Clue he gained from that encounter to place that Clue on this card. Then, if there are Clues on this card equal to the number of Investigators, the Lead Investigator gains the Key to Carcosa Artifact.
..."

You simply resolve a Research Encounter, choose not to put any Clues from that Encounter on the Mystery (because there are already enough on it) and proceed to the then part and give the Lead Investigator the Key to Carcosa.

Another, very nice way to do it is to use "Advance the Active Mystery" effect to place a Gate on the Mystery. You can do this, because the Rules allow you to choose the Token that is placed on the Mystery, as long as it is mentioned on the Mystery itself. You can even do this when there are fewer Clues on the Mystery then the number of Investigators.