To experience regret on account of; to lose or miss with a sense of regret; to feel sorrow or dissatisfaction on account of (the happening or the loss of something); as, to regret an error; to regret lost opportunities or friends. [1913 Webster]
"Calmly he looked on either life, and here
Saw nothing to regret, or there to fear." [1913 Webster]
"In a few hours they [the Israelites] began to regret their slavery, and to murmur against their leader." [1913 Webster]
"Recruits who regretted the plow from which they had been violently taken." [1913 Webster]

regret, v. & n.
--v.tr. (regretted, regretting) (often foll. by that + clause)
1 feel or express sorrow or repentance or distress over (an action or loss etc.) (I regret that I forgot; regretted your absence).
2 (often foll. by to + infin. or that + clause) acknowledge with sorrow or remorse (I regret to say that you are wrong; regretted he would not be attending).
--n.
1 a feeling of sorrow, repentance, disappointment, etc., over an action or loss etc.
2 (often in pl.) an (esp. polite or formal) expression of disappointment or sorrow at an occurrence, inability to comply, etc. (refused with many regrets; heard with regret of her death).

Idiom:
give (or send) one's regrets formally decline an invitation.

Etymology:
ME f. OF regreter bewail

N  discontent, discontentment, dissatisfaction, dissent, disappointment, mortification, cold comfort, regret, repining, taking on, heart-burning, heart-grief, querulousness, hypercriticism, inquietude, vexation of spirit, soreness, worry, concern, fear, malcontent, grumbler, growler, croaker, dissident, dissenter, laudator temporis acti, censurer, complainer, fault-finder, murmerer, cave of Adullam, indignation meeting, winter of our discontent, with what I most enjoy contented least, discontented, dissatisfied, unsatisfied, ungratified, dissident, dissentient, malcontent, malcontented, exigent, exacting, hypercritical, repining, regretful, down in the mouth, in high dudgeon, in a fume, in the sulks, in the dumps, in bad humor, glum, sulky, sour as a crab, soured, sore, out of humor, out of temper, disappointing, unsatisfactory, frustrated (failure), Int, so much the worse!, that won't do, that will never do, it will never do, curtae nescio quid semper abest rei, ne Jupiter Quidem omnibus placet, poor in abundance, famished at a feast.

VB  be discontented, quarrel with one's bread and butter, repine, regret, wish one at the bottom of the Red Sea, take on, take to heart, shrug the shoulders, make a wry face, pull a long face, knit one's brows, look blue, look black, look black as thunder, look blank, look glum, take in bad part, take ill, fret, chafe, make a piece of work, grumble, croak, lament, cause discontent, dissatisfy, disappoint, mortify, put out, disconcert, cut up, dishearten.

N  regret, repining, homesickness, nostalgia, mal du pays, maladie, lamentation, penitence, bitterness, heartburning, recrimination (accusation), laudator temporis acti, regretting, regretful, homesick, regretted, much to be regretted, regrettable, lamentable, regrettably, unfortunately, most unfortunately, Int, alas!, what a pity!, hang it!, 'tis pity, 'tis too true, sigh'd and look'd and sigh'd again, I'm sorry.

VB  regret, deplore, bewail, repine, cast a longing lingering look behind, rue, rue the day, repent, infandum renovare dolorem, prey on the mind, weigh on the mind, have a weight on the mind, leave an aching void.

N  penitence, contrition, compunction, repentance, remorse, regret, self-reproach, self-reproof, self-accusation, self-condemnation, self-humiliation, stings of conscience, pangs of conscience, qualms of conscience, prickings of conscience, twinge of conscience, twitch of conscience, touch of conscience, voice of conscience, compunctious visitings of nature, acknowledgment, confession, apology, recantation, penance, resipiscence, awakened conscience, deathbed repentance, locus paenitentiae, stool of repentance, cuttystool, penitent, repentant, Magdalen, prodigal son, a sadder and a wiser man, penitent, repenting, repentant, contrite, conscience- smitten, conscience-stricken, self-accusing, self-convicted, penitential, penitentiary, reclaimed, reborn, not hardened, unhardened, mea culpa, peccavi, erubuit, salva res est, Tu l'as voulu, Georges Dandin, and wet his grave with my repentant tears.

VB  repent, be sorry for, be penitent, rue, regret, think better of, recant, knock under, plead guilty, sing miserere, sing de profundis, cry peccavi, own oneself in the wrong, acknowledge, confess, (disclose), humble oneself, beg pardon, turn over a new leaf, put on the new man, turn from sin, reclaim, repent in sackcloth and ashes, (do penance), learn by experience.