Ivan Rakitic’s fine first-half goal proved enough to give Valverde’s men a second victory over their rivals in the space of four days, having comfortably come through their Copa Del Rey semi-final clash.
Tempers almost boiled over late in the first half when Lionel Messi looked to have been caught by a stray arm from Los Blancos captain Sergio Ramos.
Real, though, created few decent openings and are now winless in their last six league games against their El Clasico rivals.
However, Valverde is not about to put the champagne on ice just yet.
‘We still have a whole world in front of us. We know Madrid can win a lot of consecutive games, Atletico Madrid are still there too,’ the Barcelona coach said.
‘Until (the title is) mathematically secure, we will keep battling.’
Valverde added at the post-match press conference:
‘We respect our rivals, like they do to us. You have to keep fighting, if you think about it, you start losing.
‘Madrid are there, there are many days left and we have to foresee that Madrid will recover and will cut our lead.
‘You always look at second place, and also Atletico are a very solid team, but there is a lot of the league left.’
Valverde would not be drawn on the clash between Messi and Ramos.
‘Leo is fine, he has made a great effort, like everyone,’ the Barcelona boss said.
‘The referee? I have not seen anything on TV and I have no idea. It has been a hard, difficult game, a Clasico.’
Real Madrid coach Santiago Solari refused to throw in the towel on his side’s domestic hopes.
‘The league is always important, the team will compete until the last date, they always compete, no matter the distance,’ he said.
‘We played as a team, it was a game hard fought and we matched them in almost everything. We looked for it in every way and we could not score.
‘Football is pretty simple sometimes, it’s a good metaphor for life.’
Solari had recalled Gareth Bale to the starting line-up, but the Wales forward faded out of the match and was eventually substituted after the hour.
He tried, like everyone else,’ the Real Madrid coach said.
‘We played as a team, if something we did well, it was to play together, to attack, defend.’
Bale was whistled by some sections of the home support, while playmaker Isco was applauded when he finally came on for the closing stages.
Solari said in his post-match television interview with broadcaster Movistar Partidazo:
‘I think Bale has done a lot of things for this club and a lot of great things.
‘Everyone deserves respect because they have done a lot for the club, but the fans are sovereign.’