Arbeloa has been accused of mistreating the veteran after starting him from the bench for recent games.
Ahead of their meeting with Real Betis on Friday, Arbeloa said: "My answer was serious and curt. I found the question out of place. You can ask anyone how I talk about Dani Carvajal. What you're trying to do is unjustified.
"Carvajal is doing very well. He's important both on and off the field. I've said more than once that he's the club's most important academy graduate. I've always had a great relationship with him. I've always treated him with respect. For someone to think that I make lineups for personal reasons... I find it hard to believe that a coach would make lineups for anything other than footballing reasons."
Arbeloa continued: "The reason Dani isn't playing is that only 11 can play. That's why I say I am, and have to be, unfair to the players. I see them training and many of them do a great job. That's all there is to it. That doesn't mean I'm not happy with the players' work."
On Carvajal being handed a new deal, Arbeloa added: "Regarding his future, I can only say that whatever makes the club and the player happy will be fine."