I do not think Katniss ever loses her innocence in The Hunger Games.

She does kill, but only when forced to do so to save herself or someone else. Katniss kills the boy from District One to save Rue. Cato is threatening to kill Peeta when she fires the arrow that sends him over the edge of the Cornucopia. She later uses her last arrow to shoot him after he spends all night being tortured by mutts. Katniss even now feels sorry for her enemy.

Pity, not vengeance, sends my arrow flying into his skull.

She also plays for the cameras in her relationship with Peeta. Katniss never appears to have any deep feelings for him, other than not wanting him to die. Most likely she would feel that way about anyone she was partnered with in the arena.

Another reason I don't think she ever loses her innocence is because she will be mocked by the other tributes in Catching Fire for being so innocent.

I might argue that Katniss wasn't completely innocent before competing in the Hunger Games.  Katniss comes from District 12, which is poor to begin with; however, Katniss is from the poorest part of that district.  She's been having to hunt for food for herself and her family for years.  Her mother is present, but is often overwhelmed, so Katniss is basically the only care provider for her family.  She's been putting her name into the lottery system multiple times over for many years.  She's definitely not an innocent babe in the woods.  

I do believe that Katniss furthers her loss of innocence over the course of the novel.  One very concrete example of that is the fact that Katniss kills other combatants during the competition.  She's never killed a human being before, and during her time in the arena, she kills multiple people.  Another example is Rue's death.  Katniss feels like she is responsible.  Lastly, Katniss is completely conscious of the fact that she is using the "romantic" relationship with Peeta as a way to gain an advantage in the Hunger Games.  Through that, Katniss realizes that sexuality and romance sells.   

He grabs my hand away."What do I care. I've got you to protect me now," says Peeta, pulling me to him.

"Come on," I say in exasperation, extricating myself from his grasp but not before he gets another kiss.