The draw sees Real now just four points ahead of Barcelona on the table.
Karanka said: "Our players gave it all in 95 minutes and had many chances to score throughout the match. The crowd was there for us and the only thing we said in the dressing room after the game was that we must now focus on our next match.
"The squad wants to play the next game. The players are looking forward to winning and continue working hard. The only thing left to do when wearing this shirt and crest is to keep fighting.
"There were 80,000 people at the stadium, but if it is us who mention the referees anything can happen. There is little left; all that matters. The squad is united and looking forward to it. We have chances to win the title and we want to play to the end."