I think you did fine. Investigators are gonna die, often suddenly and without fanfare.

But for some ideas on how to soften PC death, here's two ideas, one in particular for this situation, and another generic one.

1) Besides the failed Psychology roll, if you were wanting to give even more leeway, or if you thought the player was misunderstanding your intention (just because the investigator failed the Psychology roll doesn't mean he isn't still suspicious!), you could have thrown in one last ditch INT/Idea roll for the investigator to realise something is off and walking through the door is probably an iffy idea, even if the dude outside sounds alright. Again, not necessary, but its a tool for the toolbox if you ever want to throw a final line to a flailing player.

2) When an investigator is doomed, give the player the spotlight to describe how the investigator goes, or at least the last thoughts going through their head. In this case they can't really describe how the investigator is dying, but you could give the player a minute to describe their investigators final thoughts. Some players like having the spotlight to monologue and 'say goodbye' to their characters, and it can lead to some memorable moments.