"I don't think a Clasico victory will give us the title", said Valverde, according to the Express.
"He is 100 per cent [fit] and that is what interests me", said Zidane.
Three second half goals from Luiz Suarez, Messi and Aleix Vidal sealed the comprehensive win for Barcelona.
Barcelona move nine points clear of nearest challengers Atletico Madrid, ahead of third-placed Valencia's match against Villarreal.
To recover from Neymar's departure to Paris Saint-Germain for a world record fee, Barca have become ever more reliant on the brilliance of Lionel Messi and the Argentine has responded with 18 goals already this season.More news: KeyCorp Comments on Microsoft Co.'s Q1 2019 Earnings (MSFT)
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"Tomorrow they are going to hammer me, that is football but it won't change how I think or what I do", added Zidane.
Zinedine Zidane told a pre-match news conference the five-time Ballon d'Or victor would play, but attacking flair has been sacrificed elsewhere in the Madrid line-up for a game that LaLiga's champions enter 11 points behind their bitter rivals at the top of the table.
The volume in the packed Bernabeu was cranked up when Ronaldo headed a corner in off the crossbar in under two minutes but the offside flag halted the premature celebrations. This is the best League in the world and it's very hard, but that's football.
Luis Suarez put the visitors in front in the second half with when he put the finishing touch on a stunning team goal.
However, Valverde is not getting carried away and rejected the idea Barca have the league title wrapped up before Christmas. Paulinho then headed the ball back towards goal, forcing Carvajal to make the last ditch save. "We need to take things game by game, treat it like any other game and go for the three points - nothing is in stone until the season is over".
But if he doesn't do that, it will be a hard off-season for him, with Antonio Conte likely to be available at that point and Mauricio Pochettino another possible successor.