Dat moment right after Mufasa's death.
Okay, okay, here is my reasoning for it, and what I am talking about specifically: As soon as Scar exiles Simba, he then immediately sends in the hyenas after him, just to make sure that any loose ends will be tied up and can be safely forgotten about.
And no, I am not talking about the chase scene. Right after showing Mufasa's death, I somehow doubted, even in my first viewing, that Simba would be caught as well. Plus, we already saw that the hyenas failed to catch Simba and Nala once before. Immediately after the chase, we are given a short comedic reprise in seeing the hyenas try and fail miserably to catch Simba once more before the scene fades to Scar delivering a tearful and mournful eulogy to Mufasa and Simba.
However, I am not talking about that. I am talking to the very end of the supposedly comedic scene with the hyenas. Imagine you're Simba: You just saw your dad die, and you are now convinced by your trusted uncle that it was all your fault, who then exiles you, and you just narrowly escaped being Hyena chow.
Crossing the border of the Pride Lands, most likely for the second and last time in your life, you are fleeing the only home you ever knew, and what do you hear getting shouted at you from behind?
"Yeah! You hear that! If you ever come back, we'll kill ya!"---
Remember: This was the
last thing Simba got to experience of the Pride Lands.
Although to be honest, I am not even sure if this counts as a sad scene or just as a heart-wrenching scene. Very powerful nevertheless, which is why I posted it here.