Isco hailed Real Madrid's attitude after a 5-1 thumping of Getafe on Saturday left Zinedine Zidane's men just a point behind Barcelona in the Liga title race.
Madrid's hopes of domestic supremacy looked remote six weeks ago but Barca's three-game winless run has given the chasing pack hope.
Barca host Valencia on Sunday and will extend the gap back to four points with a victory, but Isco says Madrid will be applying as much pressure as possible over the remainder of the season and are ready to pounce on any further slip-ups.
He told reporters: "The team has shown that we never give up. We were 13 points behind and now just one.
"Now we are putting the pressure on. We will compete until the end. We are Madrid and we cannot give up, ever.
"It was a complicated match at a difficult time. We came from the success of the comeback [against Wolfsburg in the Champions League], but the team was switched on from the first minute.
"It was a dangerous game. Perhaps the Wolfsburg win could have led to relaxation, but that has not been the case.
"There are five matches left, we are going to fight until the end. And we are trying to put the maximum pressure on Barcelona."