“You shall eat and be satisfied and give thanks to the Lord,” says the Torah (Deuteronomy 8:10). From here the Talmud learns that you must feel satiated or full in order to say to say birkat hamazon, Grace after Meals (Berachot 49b). If you have eaten less than your fill, you still need to say grace, but the obligation is on a rabbinic level.
If you suddenly remember that you have forgotten to say birkat hamazon, you may say it as long as you retain some feeling of fullness. Modern halachists specify ideally bensching within 72 minutes of finishing eating but, failing that, we can do so as long as we feel satiated from the meal.
A famous talmudic story tells of the angels arguing with God about how He appears to favour Israel; God answers how can He not, when they voluntarily take it on themselves to bensch even when they have not eaten enough to make them full, but just the volume of an egg or an olive. Though a sense of fullness is linked to the mitzvah of bensching, it is more elevated simply to give thanks for the food without feeling full.