(Disclaimer: I'm not a fitness expert; I'm just writing my own personal observation).
> People tell me this all the time, but when I exercise I just feel tired afterwards?
Okay, to normalize the discussion, consider stationary biking. For me I get the aforementioned high only when I exercise for atleast 30 minutes.
If I do it for just 20 or 15 minutes (instead of > 30 minutes), then as you said I just feel tired rather than good. I guess there's some threshold before you start feeling good, and this is probably different for different humans. Being the petrolhead that I am, I think of it like a turbo-lag followed by the turbo-kick.
> it only happens to people who are fit
I'm definitely not fit (though I'm not obese either) :)
> who have a history of exercising regularly?
No there's a tolerance thing I think, based on what I read in [1]. So in the long run you need to exercise more to get that same level of feeling good.
[1] https://www.fastcompany.com/3025957/what-happens-to-our-brai... (I don't know whether or not the person who wrote this article is an expert.)