Barcelona made the most of their rivals' latest loss, beating Real Sociedad 4-2 on Sunday.
That restored Barca's nine-point lead at the top and left Zinedine Zidane's fourth-placed side 19 points behind.
Despite that huge margin, Valverde said there was no way Madrid had given up hope of winning the title.
"Maybe Real Madrid can see other teams are closer on the table and they say that but I don't think any team has already given up on La Liga," he said.
"I wouldn't give up and I think they haven't give up yet."
The win at the Anoeta, set up by a Luis Suarez brace, was Barca's first in eight league games at the ground.
WHAT— FC Barcelona (@FCBarcelona) January 14, 2018
Barca had to come from 2-0 down and Valverde was pleased with the way his team responded to falling behind.
"It's true that during the first half Real Sociedad were better than us but it's also true we started in a good way. We had the first chances," he said.
"They were effective on their first opportunity and we suffered after that because it's difficult to win here. They started to believe again and they pushed us a lot.
"They are a good team and they were dangerous against our keeper. But the goal we scored before half-time helped us a lot and during the second half we were determined to win and we went for it.
"We believed in ourselves despite knowing that we were in a difficult stadium and against a rival, who has won over us many times before and a team who know how to play football really well."