The previous post was dead on. The soliloquy that was cited in the previous post is a great reference point for the regret that Macbeth experiences. In using that, I would like to take the question into a different direction. In his book, "The Book of Laughter and Forgetting," Milan Kundera introduces a word that might play quite well here in his definition of the term of, "Litost:" Litost is a nearly untranslatable Czech word, a state of feeling miserable and humiliated. “Litost is a state of torment created by the sudden sight of one’s own misery..." The beauty of the speech is that it can really play into the idea that regret, loss, anguish, nihilism, and a complete repudiation of one's own sense of autonomy is present in Macbeth. There is a sense that one gets in the speech indicating that Macbeth has gained a sense of insight into his own pathetic state, one that reveals a brutal combination of regret, hurt, and despondency. Within this, Macbeth experiences his own moment of "Litost," within which regret is a vital part.
Despite the fact that he has been told he can't be killed by any man born of woman, he has known from the moment he killed Duncan that he will die a violent death. "Blood will have blood, they say."
In Act V, scene 3, he laments the fact that he will not grow old gracefully and enjoy the benefits of old age, ..."As honour, love, obedience, troops of friends,/I must not look to have..." He is well aware that the actions he has taken to get the crown and to keep it condemn him to a bloody and violent death.
Perhaps the bleakest speech in the play is found in scene 5, the "Tomorrow" speech. This speech about life and time is brilliantly constructed. The last word of each line sums up the entire speech---word, tomorrow, today, time, fools, candle (a measurement of time), player, stage, tale, fury, nothing. He realizes that all he has done has led to nothing.
Macbeth is not an evil man but a man tempted by evil. Despite the fact that he knows where his actions will lead, he yields to this temptation. Once he murders Duncan, there is no turning back for him and he must keep on killing to retain what he has gained.
When he is confronted by Macduff, he tells him that he has avoided him because, "....My soul is too much charged/With blood of thine." He does regret killing Macduff's family.
Evidence of his regret can be found throughout the play since Macbeth is a good man gone bad. He constantly debates with himself about the course he has chosen.
There are several times in Act 5 when Macbeth suggests that he regrets the course of action that he has followed. The most prominent is in Scene 5:
Life's but a walking shadow; a poor player, that struts and frets his hour upon the stage, and then is heard no more: it is a tale told by an idiot, full of sound and fury, signifying nothing.
Macbeth realizes that his deeds have led to nothing but destruction and torment. It seems that he knows that he will soon fall to the approaching army, but he resolves to continue to fight simply to see his plan through to the end. Macbeth hangs on to a sliver of belief in the witches' prophecy that he cannot be harmed because he thinks all people have been born of woman. But this belief appears to be a veil for Macbeth's inner fears of being defeated. So, Macbeth does appear to have regrets about his course of action because his actions have led to his downfall.