Last night I had a dream were i wasn’t sure if i was lucid or not. When I woke up… I remember in the dream i did my reality checks and i could stretch the skin on my hand pretty far and i could breath while pinching my nose but for some reason I dont think it clicked that i was dreaming because when i woke up it just felt like a normal dream… when you wake up from a lucid dream is it meant to feel like it was a real day that just happened yesterday? or is it meant to feel like a normal dream… Im really confussed…
In my experience, sometimes LDs will feel like NDs after I wake up; especially as the day goes on. This is especially true with low level lucidity. After my first LD, I kindve had that same thought. I know I was lucid, but a day or so later, it felt kind of like a ND. I then realized that realistically, remembering yesterday feels like remembering a ND as well. 
Anyways, I’m not sure if you were lucid or not (my guess would be low level lucidity)-- it all depends on wether you knew you were dreaming or not. But I hope that I at least helped a little bit. 
As Faith said, it depends on your consciousness level. Some lucid dreams are really vivid and real, the others are just like ND’s. Sometimes you feel like you’ve really been there at that moment, sometimes it feels like an old memory.