Real's goals came in the second-half via a Kylian Mbappe penalty and Raul Asencio effort.
After the nervy win, Arbeloa acknowledged the home support were whistling and booing Vinicius Jr in the first-half.
He said, "You know I've always had a lot of respect for the Bernabéu. I've been booed a lot too, and what makes us great is the high standards of this club, and we always have to take it in stride because they know we can give much more and live up to the expectations of Real Madrid. We have to give them much more, especially this week.
"For me, as Real Madrid's coach, it's very clear. I'm going to work to get the best out of Vinicius. I'm going to demand that my players look for him. He's fearless, he has character, he's defended this club tooth and nail, he's one of the most unpredictable players, if not the most unpredictable, in the world.
"What this player has done as a kid at Real Madrid is something few have achieved. He's going to win us many titles, as he already has."
Arbeloa added: "I don't think they boo him every game. I have a lot of respect for this crowd because their high expectations push players to give their best. Nobody should forget what Vini has done here; he's carried the team on his back and won us titles. He's one of us and he'll continue to be for a long time."
On the first half performance, he continued : "We knew how difficult the match would be; it's not easy. I've also played a match after a big disappointment, and it's not easy either. It was a match with players who carried a lot of responsibility.
"We have to do things much better than we did in the first half. We have to work hard, and this match has shown us that we have to do many things much better."