The Real Madrid defender was unable to prevent his side from slipping to a shock 1-0 defeat against Espanyol last night.
The result leaves Los Blancos third in the table – 14 points behind Barcelona who also have a game in hand.
But Varane does not think that the title race is over yet and he insists that his side will fight until the very end.
The 24-year-old also admitted that Real are more focussed on beating Paris Saint-Germain in the Champions League next week, which led to their surprise loss to Espanyol.
“We won’t throw in the towel for the league,” Varane said.
”We are missing consistency. It’s happened to us a lot.
“There’s no clear explanation.
“We played well in the first half, then it went downhill.
“We don’t play together. The second half was bad.
“I don’t think that this affects the PSG match, as sometimes we are capable of the best and others the worst.
“We know that the PSG game is very important.
“The Champions League is the aim and we will give our all.
“The attitude can’t change, we have to give our all in every game.”