means A feeling of sorrow or disappointment over something you did or failed to do, wishing it had gone otherwise.

from From Old French 'regreter,' to bewail or lament the dead — to cry out in mourning. The second part may be linked to Old Norse 'grata,' to weep or groan (a cousin of English 'greet' in its old Scottish sense of weeping). So at its root, regret is literally a sound of grief: the wail you give over what is lost or beyond recall.