The French star started on the bench and came on in the 69th minute in place of Gonzalo Garcia, who had opened the scoring earlier in the match. Mbappe was met with whistles from sections of the Santiago Bernabeu crowd when he entered the pitch.
Speaking after the game, Mbappe said he had been informed by Arbeloa that he was behind Vinicius Junior, Gonzalo Garcia and Franco Mastantuono in the attacking pecking order.
"I'm well, I'm one hundred per cent," Mbappe said. "I didn't play because the coach told me I'm the fourth-choice forward behind Mastantuono, Vinicius and Gonzalo. I accept it and play the time I'm given.
"I was ready to start. I'm not angry with the manager. You always have to respect a coach's decision. I'll work hard to get back into the starting lineup."
Arbeloa quickly rejected the suggestion that he had labelled Mbappe as the club's fourth-choice attacker.
"I wish I had four forwards," Arbeloa said. "I certainly didn't say anything like that to Mbappe. Maybe he misunderstood me, but at no point did I tell him he was the fourth-choice forward."
The Madrid coach explained that the decision was linked to Mbappe's recent fitness situation rather than his standing in the squad.
"I'm the coach and I decide who plays," Arbeloa added. "A player who wasn't on the bench four days ago should not start today. It wasn't a final or a do-or-die game. That's all. I don't have any problem with anyone."
Mbappe also addressed the reaction from supporters after being booed by parts of the Bernabeu crowd.
"It's life," he said. "You can't change people's minds when they're angry. I shouldn't take it personally. That's the life of a Real Madrid player, especially a famous player like me."
The forward then appeared to send another message to his coach as he vowed to fight for his place in the team.
"Everyone has their own ideas and philosophy," Mbappe said. "I have to work to be better than Gonzalo, Mastantuono and Vini to get playing time."
