I went for many years without using any real after-shave lotion, or if I did use something, I used the horrible alcohol based "old school" after shaves (horrible idea). I always hated shaving and it too frequently left my face feeling raw or irritated.
Then, one day, I tried some Nivea For Men After Shave Balm, and it was like a door opened to a better place. My face felt refreshed, cool, and not raw or irritated. After that, I started experimenting with other modern after-shave products, and most of them are pretty decent. Alternately, there are many non-shaving related facial moisturizers that will also do a good job, although some of them have ingredients that are a little uncomfortable if you apply it immediately post shave (this is more common in lotions that aren't specifically intended for facial use).
I would definitely recommend finding something that you like, and avoid alcohol based after-shaves. Remember, when you shave, you're not just removing hair, you're also scraping and, to an extent, removing the top layer of skin. That leaves your face in a sensitive and disadvantaged state. Putting something to replenish the natural skin oils (and skin!) that you just scrubbed and scraped off is a very good thing. If you're worried about breaking out (acne), there are products that are noncomedogenic (don't block pores) that are often recommended as not increasing acne.
I've even picked up 100% Aloe Vera gel (such as the Fruit of the Earth brand) and used that as an after-shave lotion. It works pretty well.
Everyone's face is a little different, so what works for one person may not be ideal for another. Don't be afraid to try a couple of different things until you find something that works well for you.