The Blancos assistant has expressed his pleasure at the team's performance in Sunday's Valencia rout, but hopes it can carry the form into its upcoming fixtures
Gonzalo Higuain opened the scoring after nine minutes before Angel di Maria and Cristiano Ronaldo each grabbed a double to leave Madrid cruising.
"During this season Mourinho has explained several times that we are trying to improve," Karanka told reporters after the match.
"Everything we do is to improve and it seems that we are on a good path. We have to continue this way.
The 39-year-old went on to assess his side's chances against the same opposition in the upcoming Copa del Rey second-leg tie between the two teams.
"In Valencia we showed what we can do," the 39-year-old continued. "Now, the cup will be totally different. Wednesday will be different and the fans in the Mestalla will be even more with their team.
"Our mission is to bring us closer to what we did last year [in winning La Liga]."
The former Athletic Bilbao defender then critiqued the performances of Iker Casillas and Di Maria, two players who have both been on the receiving end of criticism in the press in recent times.
"What Di Maria had could not have been physical but rather a psychological click. We expected him to return to be the same as always. Tonight we saw the Di Maria we all know and want to see.
"The debate [about] Casillas has not existed amongst the [Madrid] coaching staff," he added.