Akali's kunai heal is basically near full or full energy, which means she can't spam it forever. And since you always had the advantage, she chose to play it safe and not die. What counterplay you want in this case? To constantly kill her so that she can't even be in a lane if you so much as chose to Flash + stun combo her to death?
I don't think you know what counterplay means in this case.
Counterplay =/= counterpicked
No champion should feel like they've lost the lane from champ select. That would've been her game if she didn't have a valid way to deal with you, without actually having to beat you with brute force when she clearly couldn't. At least, not that early into the game.
She was being bullied by you so she had an option to make sure she doesn't die if she can't get a kill. That sounds like a valid option to me, instead to opt for gameplay that revolves around absolutely decimating your lane opponent or failing once and not even being a factor in the game. If that interaction sounds boring to you (because it's not a clusterfuck at mid), you could've ulted on some other lanes and chosen to roam and make a difference there while leaving Akali to her own devices.
Furthermore, her AoE waveclear is her Q and it has to be leveled or filled with AP first. She can't CS properly either so her smokescreen safety net isn't a completely foolproof option to be sitting under a turret and taking no damage from poke. I've played Akali, i know her weaknesses. The way you describe them is basically you not taking an advantage of her passive gameplay and influencing other lanes because you likely wanted to prove that you were better by getting kills.
Her passive is also negated by your own, which means that if you rotate your spells, you can potentially block 2-3 passive applications from her, severely cutting down on her poke damage. You weren't an easy matchup for her and she had an option to deal with it instead of having to concede her own lane that early.