Him leaving had to do with gaining power to combat Itachi with, yes, however Naruto's fight with Sasuke was about Naruto bringing Sasuke to his senses, as well as bringing him back to Konoha.
Naruto's words may have spoken to him slightly, but that's all it was, a slight inner speaking that never actually changed Sasuke's true innitial intentions of leaveing. Naruto failed in his fight to actually bring Sasuke back both physically and mentally because: Sasuke's obsession for Itachi was stronger then the words that Naruto spoke to him. It may have dented him, but it was like that scratch on his headband, only a scratch and Sasuke's true intentions remained dead set in his heart.
Naruto scratched Sasuke's headband, and only scratched Sasuke's heart. In your speaking of the "Mental Aspect" of the fight, Sasuke still won there as well, even though Naruto's words penitrated him slightly, but not enough to actually turn Sasuke around and return to Konoha.
On a previous note, you asked how old I am, it would be polite for you to give me your age as well, please (if you don't mind)