Think of "feeling unreal" as a normal experience that everyone has from time to time. It comes to absolutely everyone -- but it comes swiftly and leaves even faster.
However, when you focus on "feeling unreal" -- just like when you focus for a long time on a word, for example, like the word that appears in larger type below -- a distortion is after a while introduced that skews your ability to discern meaning or sense of any kind in that word.
Stare at this word (please note that you have to stare at least 30 seconds):
What happened when you stared at the word?
Didn't the word lose its meaning entirely?
Weren't you staring at meaningless squiggles on the screen?
Didn't it feel weird to have the thought that you were looking at a common English word that suddenly had no meaning to you?
Didn't it feel weird that the letters themselves started to look meaningless?
If the experiment here didn't work, try it on another word, any word -- anywhere.
The same thing happens when you focus on feeling unreal.