Fullback Sergio Ramos raided all three points for the visitors with a powerful header on 18 minutes as Jose Mourinho's charges retained their seven-point advantage over Barcelona despite the Catalans claiming a hard-fought 2-1 win against Real Sociedad.
"This victory is important because it was a complicated match against a difficult opponent and the weather didn't help either," Karanka was quoted as saying on the club's official website after the encounter.
"We gave a very good performance and were never in danger of losing the advantage. We would have scored more goals if we'd done better in our chances."
"We have many players with character and strong personalities, and these games show it. It wasn't easy to win here and we did well to keep the final score."
Match winner Ramos conceded that Madrid were made to work hard for the win against their capital neighbours.
"It's been a tough game against an opponent that always makes things hard for us. Knowing how to suffer is also important," Spanish international Ramos was quoted as saying on the club's official website.
"What matters is we faced up to the challenge. The 1-0 score is enough to take three points. This motivates us to fight more in the league and to keep up the good work."
"The season is very long. We will continue to try enlarging our lead over the runners-up and to do things well. We truly deserved to win tonight despite how hard the match was and how difficult Getafe made things for us. It's hard to take points against them and I'm very happy we took three."
"I'm very happy with the season I'm having. I'm finding balance both personally and physically, and I hope to continue performing at this level at Real Madrid for many years."
Ramos revealed his delight at Madrid's ability to convert from their set-pieces.
"We're practicing on set pieces like the one I scored from and they're working out for us. It's important to be focused in set pieces to hurt opponents in attack," he added.
"It's good to be regular throughout the season, but the merit belongs to collective work, which is what's going to help us win titles."
"Teams will not make things easy for us in the league and each game will be more difficult because they all have objectives to achieve. We must continue to work with humility because we all benefit when we win. We're doing a good job and I'm sure this dynamic will bring us much success."
Madrid are now sitting pretty at the summit of the La Liga standings on 55 points, seven ahead of second placed Barcelona.