There's never really a defining moment where he admits it, but he slowly starts to realize he has feelings, though he knows he can't act on them because of Kikyo. However, he never denies that he loves her when his opponents taunt him for having feelings for a human woman. The closest we get to a realization is in episode 26 of The Final Act when Inuyasha says "Kagome taught me how to smile ... how to trust. It's because of her that I have friends. Relying on my companions -- shedding tears for others -- true strength and kindness . . . Kagome taught them all to me. She was born to meet me. And I, too, for Kagome's sake..."