Madrid were short of options at the back, with full-backs Marcelo, Fabio Coentrao and Alvaro Arbeloa all absent due to injury, but they coped well to limit the visitors to scraps in front of goal.
"The back four played very well. Celta only had one header at the end of the match and the back four have played really well," Karanka told the club's official website.
"Sergio (Ramos) knew his position; Rafa (Varane) when he plays fulfils his role and Pepe played like he always does."
Madrid dominated for large spells on Saturday night but were grateful for slices of luck in both their goals, with first Gonzalo Higuain's cross-cum-shot looping over the unfortunate Celta Vigo goalkeeper Alvarez Sergio in the 11th minute.
Then Ronaldo made sure of the points midway through the second half after Mesut Ozil tumbled in the area following a rather innocuous challenge from defender Gustavo Cabral.
It was a comfortable, if slightly uninspiring win ahead of their Champions League clash with Borussia Dortmund next week.
"We knew that if we let them have the ball they were going to create problems because they always play with the ball," Karanka added.
"If we gave them possession, they are a team that can pass and play. We were able to exert pressure because they didn't play with the usual level of confidence."
Jose Callejon, who came on as a second-half substitute, was pleased Madrid kept the pressure on Barcelona, who restored their advantage over Jose Mourinho's men to eight points after a thrilling 5-4 win at Deportivo La Coruna.
"It was hard to create chances, but luckily we won, which is the most important thing," added the midfielder.
"In these tight matches we need to score the second goal in order to be more calm.
"We know that we can't lose more points and that to keep up with Barcelona we need to keep winning."
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