He doesn't feel the bite of the snake so much as the poison of the injury. In fact, the bite is a mere slip of a knife, like a small paper cut, and the poison is those knives stabbing his heart over and over again, and all Severus can think is please make it stop.
But he says nothing because there is no point in doing so. As Voldemort had said, this is death and he can bear it for a few more minutes and then there will be no more pain. No more anything, not even a sliver of life left in him.
He finds that he doesn't mind it as much as he thought he would have.
Of all the times Severus has predicted his death he did not foresee lying alone in the Shrieking Shack and slowly withering away from the effects of Nagini's bite.
A few more minutes...hold on just a little bit, and soon it will be alright...Merlin, make it stop… his thoughts are growing increasingly desperate.
And then Potter is next to him and the painful thoughts are slowly diminishing. Severus's vision is starting to fade and he's feeling weak and he can feel his brain deteriorating, he can feel the poison making its way to his heart. He can feel his heartbeat slowing. He feels himself dying.
He looks at Potter, into his eyes. They are very, very green.
They are Lily's eyes.
Severus has already let those eyes of emerald get away from him once. And he'll be damned if he lets them again.
"Look...at...me…" he manages to croak out, and finds himself immersed into those deep, deep eyes of pure emerald as the name Lily dies out on his lips.