I believe it comes down to this basic fact. Naruto knew Sakura was hiding something but he didn't force information out of her. He just argued with her and tried to explain why he can't just forget about Sasuke. From there he watches Sakura leave. Beyond that, yes, Naruto was dense, he couldn't figure out the rest, and he couldn't figure out what exactly Sakura was hiding from him, but that of course gets explained.
That certain piece of information Sakura was hiding caused there to be an element of suspicion in Naruto's perspective. Sakura made a blunder in saying that she didn't care about Sasuke anymore, and Naruto knew that bit wasn't true. I never said Naruto doesn't know Sakura very well. He knows her the best in fact(he was able to fulfill her fairytale imagination of being kissed on her forehead which she hated so much). It's just that there was insecurity, doubt, and hesitance on his part when he didn't accept the confession at first. He's always thought Sakura would always love Sasuke. Naruto isn't correct about everything even though he's the hero and main character. It was proven in this section and he realized the childish dreams he was pursuing with Sasuke and whatnot. A small part of that childish thinking was doubting Sakuras feelings. He couldnt accept it right away because of the timing, situation, and his insecurties and doubts that were implanted on him in the past. As I said, he was shocked about Sakura's matured love for Sasuke and how she plans to kill him. His flashbacks went back to the part one Sakura when he was being confessed to also. There are some things he didnt understand right away, and the idea that Sakura is attainable now is a scary prospect to him. He's not accustomed to this kind of love nor did he ever expect Sakura to return such feelings. His hopes were crushed in the promise of a life time scene, not his love and devotion to her, but his hopes.
I never said Naruto doesn't know sakura very well. He just doesnt understand some of the feelings she's capable of feeling towards him and this confession proves that. He's always been unconcious or too dense to see the loving way she was leaning towards him. Hopefully now he understands that fully now though. This was a huge step in their relationship, all couples fight and have their disagreements sometimes right? This just made their relationship stronger and now they have a shot at something bigger and better:)