Valverde not happy to see Kovacic picked for Clasico
The Blaugrana eased to what ultimately proved a routine win at the Santiago Bernabeu, Luis Suarez finishing a sublime move to grab the opener before Lionel Messi doubled the lead from the spot with Dani Carvajal having been sent off for handling on the line.
Aleix Vidal added a late third as Barca won three consecutive away LaLiga games against Madrid for the first time in their history.
Kovacic's inclusion over the consistently influential Isco raised eyebrows, with Zidane later explaining the Croatia international was picked in an attempt to limit Messi's impact.
But his selection did not boost the pre-game spirits of Valverde, who pointed to Kovacic's performances in Madrid's Supercopa de Espana triumph over Barca as an indicator of his quality.
Asked if he was happy about Kovacic being picked, Valverde said in his post-match media conference: "No, I don't have the Real Madrid coaching facts to decide the line-up.
"I pick mine and he [Zidane] is doing the same. Kovacic played really well in both games of the Supercopa and is a great player. So I am scared about the quality of the players and he is a great player."
100% - Mateo Kovacic is the only player with a 100% passing accuracy in the first of #ElClasico (24/24 passes completed). Calm. pic.twitter.com/GBeZ4jDZHk
— OptaJose (@OptaJose) December 23, 2017
Barca are now 14 points ahead of Madrid in the table, but such a healthy margin of victory appeared unlikely when the hosts made a strong start to proceedings in the capital.
"It's true they started with high pressure at the beginning of the game. We expected that because they reinforced the midfield," Valverde added.
"They didn't let us to start our play easily and we had to play long balls. We weren't able to play our game and it was tough trying to pass through the first line of pressure.
"We struggled to pass through that line. We had our chances, as they did, but the game was totally open without an owner. They were very dangerous on the counter-attack and we had our chances to score as well.
"It was a matter of working hard and we could take control of the game in the second half by playing closer to their goal, having more chances and finally scoring."