The phrase I'm out of energy means: I'm tired, and not energetic.
The phrase is used in various contexts, and could be used to describe mental energy or physical energy.
For example, a basketball player might be out of energy, and ask for a sub to come into the game, so he can rest on the bench.
Or, on Friday afternoon after a hard week at work, a teacher may be out of energy. This means – those essays her students just handed in? She will carry them home, and grade them on Saturday after a good night's rest. She doesn't have enough mental alertness to deal with them right now.
I'd also say that the phrase is somewhat figurative. Many times, people who say they are "out of energy," actually have could be more energetic, but they are just wanting to relax. For example, the basketball player is probably not on the verge of collapsing, but he probably won't play very good defense. The teacher probably could grade the papers if she really needed to, but it's not an ideal time to do so.
The expression could also be used to describe teams, too, and not just individuals:
After the German team scored their first two goals, the Brazilian team seemed to lose their energy.
This doesn't necessarily mean that the Brazilian team looked tired, but it could also mean that they looked discouraged, and played with no heart.
Best Answer
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.
There's also phase out:
In my experience, this not used to mean that you got lost in thought.
I think you were thinking of space out:
There's also zone out: