Karanka, speaking as Mourinho seeks an official explanation from UEFA for the five-match ban he was handed last week, claims Madrid will continue to fight for La Liga until all hope is gone.
Madrid are in action at home to Getafe on Tuesday, but with just three rounds of the season remaining, the writing is on the wall for Mourinho's side, who are eight points behind leaders Barcelona.
Nevertheless, a win at home in Tuesday's all-Madrid clash, will leave Barca needing a point at Levante on Wednesday to claim a third successive title.
"We are Real Madrid and while there is still a chance mathematically, we can't give in," Karanka said.
Madrid have recently suffered surprising defeats at home to both Sporting Gijon and Real Zaragoza, and Karanka believes such slip-ups must be avoided next season if the title is to return to the Bernabeu for the first time since 2008.
"We have dropped many points we couldn't have foreseen losing at all," he said.
"We can't be losing points in games in which we are the favourites."
Xabi Alonso came off early in the 6-2 win over Sevilla on Saturday, but the midfielder should be fit to face Getafe.
Meanwhile, Cristiano Ronaldo will be keen to get on the scoresheet against Getafe in his race to finish the campaign as the league's topscorer in both Spain and Europe.
Ronaldo hit four in Madrid's 6-2 win at Sevilla to take his season's tally to 46, and although that total is six less than Lionel Messi's 52, the Portuguese leads the Argentinian by 33 to 31 in the Primera Division charts.
Ronaldo will hope to become only the second player to score 50 goals in a Spanish season and can also break Hugo Sanchez's record of 38 goals in 38 league games.
While Madrid are guaranteed a second-placed finish, Getafe are still not safe from relegation.
Michel's men are just a point clear of the drop zone but the coach - a former Madrid idol as a player - believes they will stay up.
"I am still convinced we will survive," he said.
Despite the difficulty of tomorrow's game, Michel says his side will not sit back at the Bernabeu.
"We can't sit back and wait for them, we want to have the ball," he said.
"We'll go there to try and have possession - it's a tough match but we'll give it a go."
Juan Albin and Manu del Moral could return for Getafe, but Jaime Gavilan remains sidelined.
After the game against Madrid, Getafe face fellow strugglers Osasuna and Real Sociedad in their two final games.
