Caffeine blocks the chemical adenosine from telling receptors in your brain it's time to "hit the brakes." It plays an important role in sleep and energy transfer in your body. Studies suggest if you regularly consume caffeine, your brain eventually creates more adenosine receptors. It's a response to caffeine constantly interfering with normal function. That means if you miss your morning coffee, you can feel increased drowsiness because there are more receptors for adenosine.
The takeaway: Coffee is altering your brain chemistry, but it's probably not that big of a deal. Unless you want to kick coffee entirely, in which case it's probably going to result in you taking ibuprofen and dozing off at your desk. Though, it's worth noting expectancy may play a role in these symptoms. If you can get someone to swap out your regular coffee for decaf without you noticing, it might help. Expecting to have caffeine may decrease the impact of withdrawal. Though, that's a pretty elaborate trick to pull on yourself.