The 22-year-old marked his first start for the club with the third goal in the 3-0 win over the Segunda B side at the Nueva Condomina on Tuesday.
Arnaiz has impressed for Gerard Lopez's Barcelona B team since arriving from Real Valladolid and looked dangerous throughout on the left-hand-side of the attack, in the absence of rested senior stars Lionel Messi and Luis Suarez.
Valverde believes it is an encouraging start for the forward and was pleased to be able to give him game time, along with midfielder Carles Alena and Marc Cucurella, who also made his debut.
"He's a player with self-assuredness," Valverde said of Arnaiz. "He has the goal in his head. I believed he could help us in this game and that it's good for them [the B team players] to come and face a situation like this.
"He scored a great goal, he has a powerful shot. It's a first step. We'll see if we can help us more."
The victory puts the Copa holders in pole position to progress to the last 16 and maintains Barca's fine form this season, with the Catalans having won 12 of their 13 matches in all competitions since their Supercopa de Espana loss to Real Madrid.
"It was a typical day in the cup. The opponents had a lot of enthusiasm," said Valverde.
"In the first half, we weren't too clear. In the second, we managed to get two more goals.
"It's true they played well at times but I'm happy because the B players made their debut, we won and we have to keep going."