The Ghana international joined Los Blancos on a season-long deal from European champions Chelsea during the summer.
He has since gone on to play in a number of positions for the capital-based side, including on the left-wing during Madrid's 2-0 victory over Celta Vigo at the weekend.
"That's what you sign Essien for," Karanka told Marca. "He's a well-known player capable of playing in a number of positions.
"It was an important game after the international break and his performance was exactly what we expected from him."
Essien has made five appearances in all competitions this season.