The result saw Madrid stretch their La Liga lead over Barcelona to a whopping seven points.
Barca's disappointing 0-0 stalemate at Villarreal ensured that Jose Mourinho's charges are now clear favourites for the La Liga crown but Madrid found themselves a goal down initially at the Santiago Bernabeu.
Angel Lafita stunned the hosts in the 11th minute but Madrid soon redeemed themselves thanks to Kaka just after half an hour and further goals from Cristiano Ronaldo and Mesut Ozil in the second half put the result beyond doubt.
Speaking after the encounter during the post-match press conference, assistant manager Karanka conceded that he was not fully satisfied with Madrid's display.
"We didn't play as well as wanted, but we're happy nonetheless," he was quoted as saying on the club's official website.
"We have a very good squad. The coach has stressed this many times. And it's good to have competition amongst the players because it makes them give their all."
Former Madrid defender Karanka also paid tribute to goal scorers Ronaldo, Ozil and Kaka.
"We are all well aware of Cristiano's characteristics. His experience allows him to grow and adapt to the team's necessities. We know how the Bernabeu crowd is and what it wants. They weren't much in favour of him not so long ago and tonight they gave him a standing ovation," Karanka commented.
"He played at a high level. It's better to grow and if a player of his quality manages to grow then it's great for the team. Ozil wasn't playing at last season's level recently, but he looks fine now. Kaka scored a goal and we're all happy for him."
"What matters is that the team is fine. We continue winning and must keep it up. Half the league is still at stake and all our men will be important to us."
Karanka also had words of encouragement for Turkish schemer Nuri Sahin after the former Borussia Dortmund player was overlooked for the encounter ahead of Lassana Diara.
"It was a match for Nuri, but we decided to use Lass. There are many games left and Nuri is working very well. He will be very good for us. We give him our support. All he needs is more playing time," he added.
Karanka also played down the slight injuries sustained by midfielder Xabi Alonso and fullback Marcelo.
"Xabi Alonso and Marcelo don't seem to be seriously injured, but we'll have to see how they evolve. (Estaban) Granero's performance is no surprise; we're all aware of his quality," he remarked.
Brazilian playmaker Kaka was delighted to have registered his name on the score sheet but admitted that Madrid must keep a tighter defensive line.
"I feel fine on a personal level. I'm playing well and I'm happy for it. We have a whole week to prepare for Getafe," he was quoted as saying on the club's official website.
" I had a chance to net a header as soon as the game started and I later entered the box. We'll have to fix some things because we can't keep conceding openers. The Bernabeu has always helped us. These comebacks showcase character and the crowd feels it."
Madrid now hold a commanding seven point lead over rivals Barcelona after the Catalans could only eke out a 0-0 draw at Villarreal.