This, but there's more to it.
Shinji is a weak individual. He used the powers granted to him to create a world where he could be alone. I dunno if it was his mother acting through rei, or the angels, or lillith, or whatever, but they granted him his wish. Everyone else on the planet was killed except for shinji and Ahsuka.
Ahsuka was Shinji's responsibility. She was the only part of his dream that he had to take care of himself. He could have his wish to be alone, ONLY if he could get rid of her, someone he had feelings for.
In the end, Shinji remains weak and does not kill her, he can't even achieve his own version of happiness.
He lets her live, and in the end, Him and Ahsuka become the new Adam and Eve. Shinji is cursed not only to not achieve his dream of being alone, but also will be responsible for bringing new people into the world.