It gets more tragic. Powdered root of asphodel and infusion of wormwood are ingredients in a sleeping potion called the Draught of Living Death, which condemns the drinker to a death-like slumber indefinitely. So not only is Snape saying, “I bitterly regret Lily’s death,” he’s also saying that his bitterness and regrets are ingredients in his own living death. Since Lily’s death, he has been sleepwalking through life; he does not expect to ever again be wholly alive.
Also, in Greek myth one of the possible afterlifes was the Fields of Asphodel, the resting place of “the souls and phantoms of those whose work is done”, sometimes linked to Elysium. So he’s talking about the afterlife, too. Also, asphodel has been said to be able to allow you to see the spirits of the dead. And in the Bible, the star Wormwood was cast down in Revelation and made all the waters of the Earth bitter.
So, Snape bitterly regrets Lily’s death, her loss makes him feel as if he is no longer truly living, he longs to see her again in the afterlife, and her loss was like the end of the world to him.