chagrin
n.n. a feeling of being embarrassed or upset because you failed to do something or someone else did something better than you. It is a more formal word than 'embarrassment'.
n. a state of mental distress or humiliation resulting from a failure or a perceived slight. Often used in literary or formal contexts to describe a more profound emotional reaction than simple embarrassment.
He felt a sense of chagrin when he lost the race.
The manager felt a deep sense of chagrin after realizing the error in the final report.
The diplomat's face fell into a deep chagrin as he realized his carefully prepared speech had been leaked to the press hours before the event.
From French chagrin (“sorrow”), from Middle French chagrin (“pain, affliction”) (compare Middle French chagriner, chagrigner (“to experience sorrow”), Old French chagrin (“painful, afflicted”)), probably derived from Old Northern French chagreiner, chagraigner (“to sadden”), of uncertain origin. Likely an enlargement of Old French greignier, graignier (“to cringe, growl, be sullen, be angry, grieve over”), from Old French graigne (“sadness, resentment, grief”), from graim (“sorrowful”), related to Old High German gram (“furious, gloomy, grieved”). The initial syllable is obscure. It may represent Old French chat (“cat”) to express the idea of "lamenting or yowling like cats" (compare German Katzenjammer (“distress, frustration, depression, chagrin”, literally “cat-wailing, cat-misery”), katzbalgen (“to cat-fight”)). An alternative theory is that it came from a metaphorical use of French chagrin, (peau de) chagrain (“a type of roughened leather”), with the connection of roughness, though some dictionaries consider this to be a separate word derived from Old French peau de sagrin, from Ottoman Turkish [script needed] (sağrı, “the rump of an animal, skin for tawing”). The alteration of initial s to ch is likely due to influence from chagrin meaning "sorrow".