Real Madrid coach Manuel Pellegrini believes it would be a travesty if his team failed to win a trophy this season.
Barcelona are favourites to retain their La Liga crown while Real were knocked out of the Champions League at the last-16 stage.
Pellegrini's team and Barca look set to finish the season approximately 25 points ahead of third-placed Valencia, but that is not good enough for the former Villarreal coach.
He was quoted in Marca as saying: "For Barcelona and for us, going through a year without a single title is harsh punishment.
"Theoretically, it is more difficult for us because we did not win anything last year. We have a lot of hope that the form we have displayed in La Liga will lead to a title.
"All one has to do is look at the numbers to see there have never been two teams like this. But one has to win and we hope that is us. There is pressure on both teams to win."
Real visit fourth-placed Mallorca in a crucial encounter on Wednesday evening.