The Balearic Islands outfit currently sit seventh in the standings but are just three points behind third-placed Malaga going into the final round of the season, on Sunday.
However, Mallorca's hopes of securing European football now hinge on the outcome of their visit to the Santiago Bernabeu to face Madrid, who are bidding to become the first Primera Division side to break the 100-point mark.
"It's a b***h having to play the last game against Madrid," Caparros is quoted as saying by Marca.
"But we should go with the utmost enthusiasm and convinced that if we do things right, we have a chance.
"It is a difficult task but one which we must believe in. We must give 100 percent if we are to get a positive result."
Addressing his future with the club, Caparros added that he does not yet know if he will still be at the Iberostar Stadium next season.
"We have had discussions with [Mallorca vice-president] Lorenzo Senza Ferrer and we will continue talking next week," he added.
Caparros arrived in Palma last October, succeeding Miguel Angel Nadal in the hotseat after he had stepped in following the departure of Michael Laudrup the month before.