Karanka had expected Atletico to prove tougher opponents because of their good start to the season.
"It was a hard match in the sense that they have been playing well and with a lot of confidence. Everyone thought this was going to be the year that they could beat us. But the team has showed character.
"In the first half we controlled the game and in the second we created chances.
"Wins always strengthen the group but a team like Real Madrid is strong in character by nature.
"For us it was just another match given the points difference."