Real won thanks to a successful penalty from Kylian Mbappe scored ten minutes into injury-time.
Afterwards, Arbeloa said: "I'm no Gandalf the White. What I wanted from my players is what I'm seeing: commitment and attitude.
"The effort they showed today has to continue. This is Real Madrid, and we need to do more than the other teams to win. I'm sure Valencia will play the game of the year at home, and to win it, we'll have to play very well."
On the home fans jeering, he also said: "I will always respect the Bernabéu crowd. I understand where we've come from and where we were. From there, the players have shown a very strong mentality.
"We have to keep working. There's nothing else to it."
On the penalty, Arbeloa added: "I did agree with the sending-off (Pathe Ciss), I've been told the penalty was clear, and the nine minutes of added time should have been longer.
"There are teams that need a minute just to take a goal kick at the Bernabéu."