The Spaniard highlighted the importance of the team's rearguard during their victory, while also explaining the reason Kaka was replaced at the start of the second half
Midfielder Michael Essien and youngster Raphael Varane impressed against the Primera Liga minnows, and drew praise from Jose Mourinho's backroom team.
"The back four played very well. Celta only had one header at the end of the match," Karanka declared to reporters after the match.
"Ramos knew his position, Varane fulfilled his role and Pepe played like he always does.
"We signed Essien because he is a player that the manager knows very well, and because of the various positions he can play in, which he fulfilled well tonight too.
"Today was an important match after the international break and the response of the team as a whole is what we expected."
Meanwhile, there is likely to be further speculation about the future of Brazilian playmaker Kaka after the 30-year-old was hauled off at half-time during the game.
However, Karanka played down any talk of the former AC Milan midfielder not being favoured, claiming his switch at the break was purely down to technical reasons.
"The substitution was due to a decision to employ a more standard system with [Angel] Di Maria and [Mesut] Ozil," he explained.