Unless it's something the kids say these days, I don't think that usage is correct. It could also be a regional quirk. Is it universally understood? Maybe. I could guess what you were trying to say, but I didn't really think it was idiomatic.
Like you said, the dictionary doesn't seem to support this.
Definition of faze
: to disturb the composure of : disconcert, daunt • Nothing fazed her. • Criticism did not seem to faze the writer.
There's also phase out:
If something is phased out, people gradually stop using it.
They said the present system of military conscription should be phased out.
In my experience, this not used to mean that you got lost in thought.
I think you were thinking of space out:
Definition of space out
: to become inattentive, distracted, or mentally remote • spaced out halfway through the lecture
There's also zone out:
1. To lose focus or stop paying attention to something, usually unintentionally. The term can be used to indicate that someone has focused on one thing to the exclusion of all other stimuli. I think I must have zoned out during that lecture, because when it was over I realized I didn't remember anything the professor said. Jerry kind of zones out when he plays video games, so you have to be really loud to get his attention.