The Frenchman, who missed Sunday's 2-0 defeat by Barcelona and was booed by his own fans on his return from a hamstring injury, came off the bench in the 68th minute after Arbeloa opted to play Vinicius Junior and Gonzalo Garcia in attack.
Mbappe told reporters fitness was not an issue.
"I’m 100% fine. I haven’t played because for the coach I’ve been the fourth striker in the squad behind (Franco) Mastantuono, Vini and Gonzalo," he said.
"I was ready to start, it’s his decision and it always has to be respected.
"I have no problem at all with Arbeloa. You have to accept the coach's philosophy and I have to do better to play ahead of Vini, Gonzalo and Mastantuono."
Mbappe has faced criticism from fans for travelling to Sardinia while recovering from his injury, though he said the club had authorized the trip.
Arbeloa said there was no way he could start Mbappe after he missed the Barcelona match and dismissed the suggestion he had told the Frenchman he was fourth choice.
"I had a conversation with him before the game and I don't know what he could have interpreted," the Spaniard told reporters.
"For me it is very clear that a player who four days ago could not be on the bench (against Barcelona), today should not start. Especially because it's not a final, it's not a game of life or death."
Arbeloa added that Mbappe would start Real's next match at Sevilla on Sunday.