It was a black-and-white film where a guy survives by hiding in a vault in a bank. When he comes out everything is in ruins, but some of the books from the library are not. He says, "Hello? W-Where is everybody? I...I'm the only human left. Well, at least I have my books." (With some books, he walks down some steps and then reaches for a book. His glasses fall and the lenses smash to pieces. He starts to panic not scream.) "NO, NO THA.. THAT... THAT'S NOT FAIR THATS NOT FAIR. That's not fair." (Begins to cry.) "There was time now." And then we are shown some aliens with antennas (which the people who came up with the stuff used TV antennas).
That sounds exactly like the famous Twilight Zone episode "Time Enough at Last". According to Wikipedia, the final speech is