The quality of "irritation" falls on the mild end of the anger spectrum: it's not quite frustration and it's nowhere near rage, but the fact that it's so mild almost makes it worse than either because there's no emotional response adequate to process it. It feels ridiculous to be mad, but it's unsatisfying to laugh, and so you're just stuck with the fractured feeling of irritation ... a kind of mild infuriation, as it were.
One way to approach this feeling is perspective: cataloguing all of the mildly infuriating things that happen throughout the day, either expectedly or unexpectedly, and being mindful that they are as seemingly integral to creation's matrix as joy or kindness. Luckily for you, there's a tool for that — namely the Mildly Infuriating subreddit, where we found these delightfully irritating examples.
Enjoy. Or don't.