Similarity in the look of words can influence their meaning. Words in English that look and sound alike sometimes slowly converge. Copyeditors are left to ask whether the new meanings are fine and understood or whether they create a distraction.
This is true of discomfit, which looks an awful lot like discomfort, even in the context of a sentence. Dictionaries and usage guides accept discomfit in the sense of making someone feel embarrassed or otherwise uncomfortable. That’s the more-likely word if you’re looking for a verb, and its use goes back hundreds of years. You can discomfort someone, but it’s more accepted that you would discomfit someone.
In Middle English, discomfit meant defeat in battle. That meaning remains in the sense of frustrating someone’s plans. But the newer meaning is now more common, and there is no reason to cling purely to the original form.
Discomfit can be traced to the Old French desconfit, from the prefix dis- attached to conficere, meaning put together. Take off the prefix, and we have comfit, a candy treat. Conficere also gave us confection, another tasty thing or simply the result of things that are put together. Con, meaning with or together, shows up in many words, such as contract. (But the word con, the opposite of pro, comes from the Latin contra.)
Comfort starts with the Latin fortis, or strength. With the prefix, it originally meant to strengthen, which is still found in the modern verb form. As a noun, comfort means physical ease, but it also is the consolation we receive in the face of loss.
You also could disconcert someone. The word concert has the sense of a bringing together of sounds for a musical performance. Disconcerted, discomfited, and discomforted pretty much mean the same thing, as upsetting as that may be.