‘And Yahweh regretted that he had made man on the earth (or “the men in the land”) and it grieved him to his heart.'
This anthropomorphism is a way of demonstrating God's regret at the situation. It is because man has altered the situation that it arises. It is not that God is changing His mind because He thinks He has made a mistake. The change of mind comes because man has drastically changed, and He is grieved by it. He would have wished for anything but this. But having given man the freedom to sin the consequences have to be dealt with.
“It grieved him to his heart.” He was sad at what man had become. Thus unlike the gods of other nations he is concerned about man's condition.
There is an interesting parallel between this verse and Genesis 5:29. It was said of Noah ‘this one shall bring us relief (nchm) from our work (‘sh) and from the toil (‘tsb) of our hands'. Here we have ‘it grieved (nchm) him that he had made (‘sh) man and it pained (‘tsb) him to his heart'. How different was the immediate fruit from the promise. But it also reminds us that the world is divided into two. Those who are blessed by God because they are His and those who break His heart and face judgment.