Jose Arnaiz gave Barca the lead in the 15th minute at Balaidos, but Pione Sisto slammed home an equaliser before half-time.
Ousmane Dembele came on in the final 20 minutes for his first appearance since September, but the game ended 1-1, leaving everything to play for.
Celta earned a 2-2 draw at the Catalan giants in La Liga last month, a result that would be sufficient to send them into the quarter-finals if repeated next Thursday, leaving head coach Valverde wary.
"It's another competition and we know Celta's quality. They showed it in La Liga and again today," the Barca boss said.
"They will come to play and we will too. We know the quality they have from La Liga. We respect them a lot.
"Everything is yet to be decided."
Valverde left out stars like Lionel Messi, Luis Suarez, Andres Iniesta and Jordi Alba, but was pleased with what he saw from those who came into the starting XI.
He said: "There have been changes from the last La Liga game, but many of the players who played today have been playing and doing well.
"I'm happy with the squad I have. I think it's deep and that there are players who can help us in many moments."
Barca B forward Arnaiz was pleased to be given the chance to play with the first team again and make an impact by scoring his third Copa del Rey goal of the season.
"I'm very happy, not because of the goal, but because of how the team did," he told BarcaTV.
"I think it was a good match because they played very well. Three goals in three games makes me feel good, but we have to keep working."