First-team coach Jose Mourinho made seven changes from the side that beat the Catalans 3-1 on Tuesday at the Camp Nou in the Copa del Rey.
But Madrid overcame an almost full-strength Barcelona side thanks to goals from Karim Benzema and Sergio Ramos in-between Lionel Messi's leveller for the visitors.
Speaking at the post-match press conference, Karanka said: "You need all your players to deliver in a big game like this, including the ones who play less often.
"Of all the performances of the team, I was particularly impressed with those players. The team have shown that, whoever is playing, they deserve to be trusted."
However, Karanka warned his players against being complacent after the consecutive victories over their biggest rivals, ahead of Tuesday's Champions League last-16 second leg encounter at Manchester United.
"We have to be happy with the result but if we think we have done something extraordinary we could end up regretting it on Tuesday," he said.
"There's no champagne here to celebrate anything, all we'll be doing is working hard while remaining excited about the rest of the season We have to keep going in the same direction."
Karanka explained that Madrid dealt with the pressure of having the three decisive games - the two with Barcelona and one at Manchester United - in such a short space of time by just focusing on their day-to-day work.
"We work hard every day and these games make us work even harder," he added. "Everyone was saying that the season could be over this week but we haven't let us affect us.
"We just work to make sure the team is as good as possible."