Radamel Falcao gave the hosts an early lead but an own goal by Juanfran levelled things up a few minutes later, and Angel Di Maria hit the winning goal midway through the second half.
"It was not a match with many chances for either side. They crossed a lot of balls into the box and we knew it was their biggest threat. Apart from a chance for Benzema there weren’t very many chances in the first half. After the tough night the other day, we’ll take away the team’s strong performance today and the good football from players who don’t usually play," said Karanka.
"We knew it would be a very tense match because we were playing for second place and because it was a derby, and as I already said, Atletico haven’t beaten us for a long time. The best way to go into Tuesday’s match was by having a good match here. This is how it was, it is what we planned to do, that is what the players knew and that is what they have done, and spectacularly well."