Carroll surely is? He's only going to get better as well.
Who should you have in charge instead? Of course people question the manager's tactics. That's what fans do and go to Man Utd, Arsenal, Barcelona, Accrington and Sunderland forums and you'll see it is exactly the same. With this game, where I and seemingly everyone else thought Hughton got it wrong, it is up to him to respond, and respond swiftly.
Also, home results this season would indicate you've had 2 poor results, not that you "haven't improved at all". Would the team from 2 years ago have come to Goodison and outplay a top 6 aiming team for large parts, for example?