He liked Sakura for years, she wasn't a bad girl or anything and she'd be willing to die for Naruto as well. How many people fall for others just because they liked you? While Hinata liked him, she really wasn't that close to him. She was willing to die for him, but so were most of the Leaf. He really seemed to love Sakura even though she might not like him, so if he really cared for her, then it'd make no sense for him to quickly get over her. Naruto isn't fickle, and Hinata wasn't really his type (he seems to like the tsundere and girl with back bone; if Hinata did have that back bone in the beginning, then she wouldn't have fallen for Naruto because the only reason she fell for Naruto was cause he was a fellow loser, except unlike her, he never gave up).
Also as a child, Sakura was ostracized (like Naruto but not to nearly the same extent) for something outside of her power and then was rescued by one person showing kindness to her and befriending her.
Another reason for Naruto to still like Sakura is because she will try almost anything to protect him. While her fake confession was mean, she did it to protect him, and she was willing to try and kill Sasuke when he joined Akatsuki (an organization that wanted to kill Naruto).
While she couldn't kill Sasuke, it didn't exactly have to mean that she still liked him; it could just be because she liked him for 5 years and then he became a part of her family (Team 7) so she couldn't kill him because of who he used to be (before Itachi mind raped him a 2nd time, he was actually a pretty good kid, though he was anti-social). So Naruto might feel that he still has a chance.
There could be a lot of reasons for Naruto to like Sakura and pick her over Hinata. These are a few I could think of. It's not like anything I'm shipping is possible anyways.