After the flood Noah offered עולות, burnt offerings, on an altar to HaShem, and HaShem accepted the offerings. And then the verse reported,
ויאמר ה' אל לבו לא אסף לקלל עוד את האדמה בעבור האדם כי יצר לב האדם רע מנעוריו ולא אסף עוד להכות את כל חי כאשר עשיתי
And HaShem said in His Heart I will not curse the land again because of mankind, because the inclination of man's heart is evil from his youth, and I will not strike every living being as I have done.
In this verse it sounds like that since mankind's nature is bad, HaShem won't punish him so harshly with total destruction. But interestingly, at the end of last week's Perashah, Perashat Bereshit, the verses said:
וַיַּרְא ה' כִּי רַבָּה רָעַת הָאָדָם בָּאָרֶץ וְכָל-יֵצֶר מַחְשְׁבוֹת לִבּוֹ רַק רָע כָּל-הַיּוֹם
And HaShem Saw that mankind's evil was so abundant in the land and how all of the inclination of his thoughts were only evil the entire day
וינחם ה' כי-עשה את האדם בארץ ויתעצב אל-לבו
And HaShem regretted that He Made mankind in the land, and He Was sad in His Heart
ויאמר ה' אמחה את-האדם אשר-בראתי מעל פני האדמה מאדם עד-בהמה עד-רמש ועד-עוף השמים כי נחמתי כי עשיתם
And HaShem said, I will wipe out mankind, whom I have created, from the face of the earth, from man to animal, to crawling creatures, to the birds of the sky, because I regretted that I made them
In these verses it sounds like the total destruction came BECAUSE of man's evil. The Abarbanel asked what changed from the end of Perashat Bereshit to Perashat Noah after the flood? How come at first man was destroyed because he was evil and now it sounds like he won't be destroyed again because his nature is evil?
One answer is that it's not practical to totally destroy the world every time humanity deserves it. Therefore the Abarbanel explained that from now on sins will be punished gradually as the next verse discussed זרע planting and קציר harvesting and קור וחום coldness and heat. Now sins would be atoned for with agricultural problems and difficult weather conditions as well as with sickness and other difficulties. The verse in Perashat Noah doesn't mean that humanity will no longer be held responsible for their actions, but rather after a one-time huge punishment, future punishments will be given in a way that preserves the existence of the world by punishing individual locations with various natural disasters. In the past they hadn't been punished gradually, so the account of humanity's sins reached the point of total destruction. But going forward, Hashem will not let us reach that point, because of gradual atonement.
HaShem made the statement about man's evil inclination to Himself (אל לבו) as opposed to Noah, since it would be counterproductive to let Noah know this. It's recorded in the Torah for us, but Noah had to think the best of himself in order to start the world anew with the proper attitude. Afterwards HaShem did tell Noah that He will not destroy the world again (9:11) without mentioning anything about man's evil inclination.
Another explanation is that just like an individual is immature when they're young and engage in foolish behavior and even sin due to their immaturity, so too the world as a whole needed time to mature. In the first stage before the flood they were like the children and teenagers that were out of control. But now in the next stage after experiencing the flood, mankind is gradually getting more mature. So according to this explanation, the verse is more of a prophecy than a statement.
ויאמר ה' אל לבו could mean HaShem was making a prophetic statement
לא אסף לקלל עוד את האדמה בעבור האדם
I won't have to curse the land because of mankind (because they won't deserve it)
כי יצר לב האדם רע מנעוריו
Because man's inclination was evil in his adolescence (meaning in the previous generation)
But now in this next stage, having experienced the dramatic punishment of the flood, and the fact that all of the world will now descend from Noah who is righteous, humanity will improve gradually and total destruction will not be necessary.
Abarbanel also offered an alternate explanation to ויאמר ה' אל לבו. HaShem did not speak to his own heart but rather about man's heart. In the past man's heart was bad but now over time it will improve.
So either there won't be another flood because Hashem will make sure that humanity won't reach the point of deserving total destruction by atoning for sin gradually through adverse weather, famine and sickness. Or the verse in Perashat Noah is referring to the wickedness of the previous generation, but after the flood mankind will mature and improve so total world destruction will no longer be warranted.